API marketplace

Wet Bulb Globe Temperature (WBGT) heat-stress index as an API, computed locally and deterministically. WBGT is the standard occupational and athletic heat-stress measure (ISO 7243). The wbgt endpoint computes the true index from measured thermometer readings: outdoors in the sun WBGT = 0.7·Tnwb + 0.2·Tg + 0.1·Tdb, and indoors or in the shade WBGT = 0.7·Tnwb + 0.3·Tg, from the natural wet-bulb, globe and dry-bulb temperatures, and returns the heat-stress flag and work-rest and hydration guidance. The estimate endpoint gives an approximate shade WBGT from just the air temperature and relative humidity using the Bureau of Meteorology approximation — e = (rh/100)·6.105·exp(17.27·T/(237.7+T)); WBGT ≈ 0.567·T + 0.393·e + 3.94 — for when you do not have a globe or wet-bulb thermometer. The flag endpoint classifies any WBGT value (°C or °F) into a heat-stress category — green, yellow, red or black — with the recommended work-rest cycle and water intake. Everything is computed locally and deterministically, so it is instant and private. Ideal for occupational-safety and industrial-hygiene tools, sports, military and outdoor-event planning, and environmental-monitoring apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the WBGT heat-stress index; for the NWS heat index, wind chill and dew point use a weather-formulas API.

Uptime

100.0%

Latency

78ms

Subs

3,101

Standing-wave and resonance maths for strings and air columns as an API, computed locally and deterministically. The string endpoint models a string fixed at both ends: from its length and the wave speed — given directly or as the tension and the linear mass density (which you can supply directly, or have computed from a mass and length, or from a wire diameter and material density) — it returns the wave speed v = √(T/μ), the fundamental frequency f₁ = v/(2L) and the harmonic series f_n = n·f₁, each with its wavelength and node and antinode count; it can also solve the tension needed to tune the string to a target fundamental. The pipe endpoint does the same for an air column: an open pipe (both ends open) resonates at all harmonics f_n = n·v/(2L) while a closed (stopped) pipe resonates only at the odd harmonics f_n = (2n−1)·v/(4L), with the speed of sound given directly or worked out from the air temperature, v = 331.3·√(1 + θ/273.15). The harmonics endpoint generates the harmonic series from a fundamental frequency, or from a wave speed and a length, for a string, an open pipe or a closed pipe. Everything is computed locally and deterministically, so it is instant and private. Ideal for musical-instrument and luthier tools, acoustics and audio apps, organ-pipe and wind-instrument design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is mechanical standing waves and resonance; for note-to-frequency music theory use a music-note API and for electromagnetic wavelength λ = c/f use a wavelength API.

Uptime

100.0%

Latency

80ms

Subs

3,405

Torricelli efflux and orifice-discharge maths as an API, computed locally and deterministically. The velocity endpoint applies Torricelli's law, v = √(2·g·h) — the speed at which fluid jets from an orifice under a head h equals that of a body that has fallen the same height — and returns the ideal and the actual jet velocity (corrected by a coefficient of velocity), and, if you give the orifice diameter or area, the ideal and actual volumetric discharge Q = Cd·A·√(2gh) in litres per second and minute, cubic metres per hour and US gallons per minute. The drain-time endpoint computes how long a vertical cylindrical tank takes to empty through an orifice, t = (2·A_tank)/(Cd·A_orifice·√(2g))·(√h0 − √h1), from the tank and orifice sizes, the starting head and an optional final head, with the initial flow rate. The range endpoint gives the horizontal distance a jet from a side orifice travels before it lands, x = 2·Cv·√(h·y), from the head above the orifice and the orifice's height above the ground, with the jet velocity and time of flight. The discharge and velocity coefficients default to 0.62 and 0.97 and can be overridden, as can gravity. Everything is computed locally and deterministically, so it is instant and private. Ideal for fluid-mechanics and hydraulics tools, tank-drainage, irrigation and process-engineering apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is orifice efflux and tank drainage; for pipe continuity Q = A·v use a flow-rate API and for tank volume and fill level use a tank API.

Uptime

100.0%

Latency

74ms

Subs

3,521

Latent-heat and phase-change enthalpy as an API, computed locally and deterministically. The latent endpoint applies Q = m·L — the heat to melt, freeze, boil or condense a substance equals its mass times the latent heat — and solves for whichever of the heat, the mass or the latent heat you leave out, taking the latent heat of fusion or vaporization directly or from a built-in substance table (water, ethanol, mercury, lead, aluminium, iron, nitrogen, oxygen). The phase-change endpoint computes the full enthalpy of heating or cooling a substance from one temperature to another, automatically combining the sensible heat m·c·ΔT within each phase with the latent heat at every melting and boiling transition it crosses, and returns a step-by-step breakdown — so it can tell you, for example, the total energy to turn ice at −10 °C all the way into steam at 110 °C, using the right specific heat for the solid, the liquid and the gas. The substances endpoint lists the latent heats and per-phase specific heats. Heat is reported in joules, kilojoules, watt-hours and kilocalories. Everything is computed locally and deterministically, so it is instant and private. Ideal for thermodynamics and HVAC tools, refrigeration, heating and process-engineering apps, food and material science, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is latent heat and phase change; for sensible heat alone (Q = m·c·ΔT with no phase change) use a specific-heat API.

Uptime

100.0%

Latency

77ms

Subs

4,542

Wheatstone-bridge and strain-gauge maths as an API, computed locally and deterministically. The bridge endpoint takes the four arm resistances R1–R4 and an excitation voltage and returns the bridge output voltage between the two midpoints, Vout = Vin·(R2/(R1+R2) − R4/(R3+R4)), in volts and millivolts, the voltage at each midpoint, and whether the bridge is balanced (Vout = 0 when R1·R4 = R2·R3). The balance endpoint inverts it: give any three arms and it solves the fourth resistance that balances the bridge, the classic way a Wheatstone bridge measures an unknown resistance. The strain endpoint models a strain-gauge bridge — quarter, half or full — and converts in both directions between mechanical strain and electrical output: from a gauge factor and a strain (given directly, as microstrain or as a relative resistance change ΔR/R = GF·ε) it returns the output ratio and voltage Vout/Vin = (k/4)·GF·ε where k is the number of active arms, and from an output voltage and excitation it returns the strain and microstrain. Everything is computed locally and deterministically, so it is instant and private. Ideal for instrumentation and sensor tools, load-cell, pressure-sensor and RTD measurement design, strain-gauge and data-acquisition apps, and electronics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is bridge and strain-gauge measurement; for Ohm's law, voltage dividers and series/parallel resistor combinations use an Ohm's-law API.

Uptime

100.0%

Latency

77ms

Subs

3,762

Flywheel and rotational-energy dynamics as an API, computed locally and deterministically. The energy endpoint computes the rotational kinetic energy stored in a spinning body, E = ½·I·ω², together with its angular momentum L = I·ω, in joules, kilojoules and watt-hours — from a moment of inertia (given directly, or worked out from a shape, mass and dimension) and an angular speed given as rpm, radians per second or hertz, which it reports in all three. The inertia endpoint returns the moment of inertia about the central axis for the common shapes — solid disk and cylinder (½·m·r²), thin ring and hoop (m·r²), hollow cylinder (½·m·(r_out²+r_in²)), solid sphere (⅖·m·r²), hollow sphere (⅔·m·r²) and a rod about its centre (1/12·m·L²) or end (⅓·m·L²) — from a mass and a radius, diameter or length. The flywheel endpoint sizes a flywheel: give a target energy and an operating speed and it returns the required inertia I = 2E/ω², or give an inertia and a maximum and minimum rpm and it returns the energy delivered between them, ΔE = ½·I·(ω₁²−ω₂²), with the coefficient of fluctuation. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering and energy-storage tools, motor, engine and powertrain design, kinetic-energy-recovery and physics-education apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is rotational energy and inertia; for bolt tightening torque use a torque API and for power-screw mechanics use a screw-jack API.

Uptime

100.0%

Latency

77ms

Subs

4,389

Banked-curve and circular-motion dynamics as an API, computed locally and deterministically. The speed endpoint takes the radius of a curve and its banking (bank) angle and returns the frictionless ideal (design) speed at which the banking alone supplies the centripetal force, v = √(r·g·tanθ); give a coefficient of friction as well and it also returns the maximum safe speed before the vehicle slides outward up the bank, v = √(r·g·(tanθ+μ)/(1−μ·tanθ)), and the minimum speed before it slides inward down the bank — every speed in metres per second, km/h, mph and knots, plus the centripetal acceleration. The bank-angle endpoint inverts this: from a design speed and radius it returns the ideal banking angle θ = atan(v²/(r·g)) and the equivalent superelevation as a ratio and a percentage, the cant a road or railway needs so no side friction is used at that speed. The flat-curve endpoint handles an unbanked curve from the coefficient of friction: the maximum cornering speed v = √(μ·r·g) for a given radius and the minimum radius v²/(μ·g) for a given speed. Gravity defaults to standard 9.80665 m/s² and can be overridden. Everything is computed locally and deterministically, so it is instant and private. Ideal for road and racetrack design tools, vehicle-dynamics and driving-simulator apps, civil and transportation engineering, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is curve banking and cornering dynamics; for projectile and SUVAT kinematics use a physics API.

Uptime

100.0%

Latency

80ms

Subs

4,050

Taper and cone geometry as an API, computed locally and deterministically. The taper endpoint relates the large and small diameters, the length and the taper of a conical part: give the two diameters and the length and it returns the taper ratio, the taper per foot and per inch (for inch parts), the included angle 2·atan((D−d)/(2L)) and the half (taper) angle from the axis — or leave one of the diameters or the length out and provide the taper per foot, and it solves for the missing dimension. The diameter-at endpoint gives the diameter (and radius) at any distance along the taper, measured from either the large or the small end, by linear interpolation d(x) = D − (D−d)·x/L. The morse endpoint is a reference of the standard Morse taper series MT0 to MT7, with each taper's taper per foot, gauge-line large and small diameter, length and included angle. Lengths and diameters use consistent units (inches by default, or millimetres for the angle and ratio outputs). Everything is computed locally and deterministically, so it is instant and private. Ideal for machining and lathe tools, CAD and toolmaking apps, maker and metalworking projects, and mechanical-engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is taper geometry; for screw-thread pitch and tap drill use a thread API and for spur-gear geometry use a gear API.

Uptime

100.0%

Latency

71ms

Subs

4,363

Thermal-expansion maths as an API, computed locally and deterministically. The linear endpoint computes how much a solid grows or shrinks when its temperature changes, ΔL = α·L0·ΔT, returning the change in length and the new length from an original length, a temperature change (given directly or as an initial and final temperature) and the linear expansion coefficient α — taken from a built-in material table (steel, aluminium, copper, concrete, glass, invar and more) or supplied directly; lengths accept metres, centimetres, millimetres, feet or inches. The volume endpoint computes volumetric expansion, ΔV = β·V0·ΔT, where for a solid the volumetric coefficient is β ≈ 3α and for a liquid (water, ethanol, mercury, petrol and others) β is taken directly; volumes accept cubic metres, litres, millilitres or cubic feet. The materials endpoint lists the coefficients. A negative temperature change gives contraction. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil and mechanical engineering tools, rail, pipe and bridge expansion-gap design, manufacturing-tolerance and HVAC apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is thermal expansion; for heat energy and temperature change use a specific-heat API.

Uptime

100.0%

Latency

74ms

Subs

4,920

pH and acid–base maths as an API, computed locally and deterministically. The ph endpoint converts freely between the four ways of describing acidity — the pH, the pOH, the hydronium-ion concentration [H+] and the hydroxide concentration [OH−]: give any one and it returns the others using pH = −log₁₀[H+], [OH−] = Kw/[H+] and pH + pOH = pKw, and classifies the solution as acidic, neutral or basic. The strong endpoint gives the pH of a strong acid or strong base from its molarity ([H+] = c for an acid, [OH−] = c for a base), warning when the solution is so dilute that water self-ionisation matters. The buffer endpoint applies the Henderson–Hasselbalch equation, pH = pKa + log₁₀([A−]/[HA]), to a buffer from a pKa and the conjugate-base-to-acid ratio (given directly or as two concentrations), and also handles a base buffer from a pKb. Kw defaults to 1×10⁻¹⁴ (25 °C) and can be overridden for other temperatures. Everything is computed locally and deterministically, so it is instant and private. Ideal for chemistry and biology lab tools, titration and buffer-prep apps, water-treatment and aquarium software, and science education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is pH and acid–base chemistry; for solution dilution and molarity use a dilution API.

Uptime

100.0%

Latency

78ms

Subs

3,949

Doppler-effect maths as an API, computed locally and deterministically. The sound endpoint computes the acoustic Doppler shift, f' = f·(v + vo) / (v − vs), where v is the speed of sound (given directly, derived from an air temperature, or the default 343 m/s at 20 °C), vs is the source velocity and vo the observer velocity, with positive velocities meaning approaching: it returns the observed frequency and the frequency shift, and refuses a supersonic source. The light endpoint computes the relativistic Doppler effect for light, f' = f·√((1+β)/(1−β)), from a velocity in metres per second or as a fraction of the speed of light and a direction (approaching blue-shifts, receding red-shifts), returning the frequency and wavelength factor, the observed frequency or wavelength, and the redshift z. The radial-velocity endpoint reverses it: from a measured redshift, or an observed and rest wavelength, it recovers the radial velocity with the exact relativistic relation and the simple v ≈ z·c estimate. Frequencies are in hertz, wavelengths in nanometres, velocities in metres per second. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and astronomy education, radar, sonar and lidar tools, audio and acoustics apps, and spectroscopy and redshift calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the Doppler effect; for sound levels and decibels use an acoustics API.

Uptime

100.0%

Latency

80ms

Subs

4,014

Arrhenius reaction-kinetics maths as an API, computed locally and deterministically. The rate-constant endpoint applies the Arrhenius equation k = A·exp(−Ea/RT), relating the rate constant, the pre-exponential (frequency) factor A, the activation energy Ea and the absolute temperature: give any three and it solves for the fourth, with the activation energy in joules or kilojoules per mole and the temperature in kelvin or Celsius. The activation-energy endpoint uses the two-point method — from two rate constants measured at two temperatures it returns the activation energy, Ea = R·ln(k2/k1)/(1/T1 − 1/T2), and the pre-exponential factor. The temperature-effect endpoint gives the factor by which the rate changes between two temperatures, k2/k1 = exp(−Ea/R·(1/T2 − 1/T1)), along with the Q₁₀ — the rate multiplier per 10 K rise — and the new rate constant if you supply the old one. The gas constant R is 8.314462618 J/(mol·K). Everything is computed locally and deterministically, so it is instant and private. Ideal for chemistry and chemical-engineering tools, reaction and process-design apps, shelf-life and stability modelling, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is reaction kinetics; for the ideal gas law use a gas-law API and for radioactive decay use a half-life API.

Uptime

100.0%

Latency

74ms

Subs

4,888

Snell's-law refraction optics as an API, computed locally and deterministically. The refraction endpoint applies Snell's law, n1·sin(θ1) = n2·sin(θ2): from the refractive indices of two media (given directly or by material — vacuum, air, water, glass, diamond and more) and the angle of incidence it returns the angle of refraction, or solves for the incidence angle from a refraction angle; when light passes into a less dense medium beyond the critical angle it reports total internal reflection instead of a refracted ray. The critical-angle endpoint gives the threshold for total internal reflection, θc = asin(n2/n1) for n1 > n2 — the principle behind optical fibres — defaulting the exit medium to air. The speed endpoint gives the speed of light in a medium, v = c/n, as a fraction of c, and — with a vacuum wavelength — the shorter wavelength inside the medium (the frequency is unchanged). Angles are in degrees, wavelengths in nanometres. Everything is computed locally and deterministically, so it is instant and private. Ideal for optics and photonics tools, fibre-optic and lens-design apps, photography and physics education, and AR/VR and rendering software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Snell's-law refraction; for camera depth of field and field of view use a photography API.

Uptime

100.0%

Latency

75ms

Subs

3,539

Calorimetry (specific-heat) maths as an API, computed locally and deterministically. The heat endpoint applies the sensible-heat equation Q = m·c·ΔT — the heat energy equals the mass times the specific heat times the temperature change — and solves for whichever of the four quantities you leave out, taking the temperature change directly or as the difference of an initial and final temperature, and the specific heat directly or from a built-in material (water, ice, aluminium, copper, steel, glass, ethanol and more); it reports the heat in joules, kilojoules, calories, kilocalories and watt-hours. The mix endpoint finds the equilibrium temperature when two bodies at different temperatures are brought into thermal contact, Tf = (m1·c1·T1 + m2·c2·T2) / (m1·c1 + m2·c2), with the heat transferred, for the same or different materials. The materials endpoint lists typical specific heats. Use SI units — mass in kilograms, specific heat in joules per kilogram-kelvin, temperatures in °C or K (the difference is the same). Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and chemistry education, thermal-engineering and HVAC tools, cooking and brewing apps, and material-science calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is calorimetry; for the ideal gas law use a gas-law API.

Uptime

100.0%

Latency

73ms

Subs

4,801

Beer–Lambert spectroscopy maths as an API, computed locally and deterministically. The beer-lambert endpoint applies the law A = ε·c·l, where absorbance equals the molar absorptivity times the concentration times the optical path length: give any three of the four and it solves for the fourth (the path length defaults to the standard 1 cm cuvette when omitted), and it always reports the matching transmittance and percent transmittance. The transmittance endpoint converts between absorbance and transmittance in both directions, A = −log₁₀(T) and T = 10^(−A), and accepts a fraction or a percentage. The calibration endpoint reads a concentration off a linear calibration curve, A = slope·c + intercept, solving for the concentration from a measured absorbance or for the expected absorbance from a concentration. Units are whatever you supply consistently — for molar absorptivity in M⁻¹cm⁻¹, a path length in cm and absorbance dimensionless, the concentration comes out in molar. Everything is computed locally and deterministically, so it is instant and private. Ideal for analytical-chemistry and lab tools, spectrophotometer and assay apps, biotech and education software, and quality-control calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Beer–Lambert spectroscopy; for solution dilution and molarity use a dilution API and for chemical compound data use a chemistry API.

Uptime

100.0%

Latency

73ms

Subs

3,983

Orbital-mechanics maths as an API, computed locally and deterministically. The circular endpoint computes a circular orbit around a body — the orbital speed v = √(GM/r), the orbital period T = 2π·√(r³/GM), the escape speed and the specific orbital energy — from a built-in body (Sun, Mercury through Neptune, the Moon) and an altitude above its surface, or from an explicit orbital radius, central mass or standard gravitational parameter. The escape endpoint gives the escape velocity √(2·GM/r) at any radius or altitude, which is √2 times the circular-orbit speed there. The period endpoint applies Kepler's third law in both directions: from a semi-major axis it returns the orbital period, and from a period it returns the semi-major axis — so a sidereal day around Earth gives the geostationary radius of about 42,164 km. Speeds come out in metres and kilometres per second and km/h, distances in metres and kilometres, and periods in seconds, minutes, hours and days. Everything is computed in SI and is instant and private. Ideal for aerospace and satellite tools, space-mission and education apps, astronomy and KSP-style games, and physics calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is orbital mechanics; for live satellite catalogues use a satellites API and for sky positions use an astronomy API.

Uptime

100.0%

Latency

83ms

Subs

4,272

Radioactive (exponential) decay maths as an API, computed locally and deterministically. The decay endpoint computes how much of a substance remains after a given time, N(t) = N0·(1/2)^(t/T½) = N0·e^(−λt): from a half-life (or a decay constant or mean lifetime), an elapsed time and an optional initial amount, it returns the fraction and percent remaining, the remaining and decayed amounts, the number of half-lives elapsed, and — if you give an initial activity — the remaining activity, which decays by the same factor. The constant endpoint converts freely between the half-life T½, the decay constant λ = ln2/T½ and the mean lifetime τ = 1/λ = T½/ln2. The age endpoint reverses the decay to find the elapsed time from the fraction remaining, t = T½·log₂(1/fraction) — the basis of radiometric (carbon-14) dating — and accepts either a fraction or a remaining and initial amount. Time and half-life share one unit, and the results come out in that unit. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics and chemistry education, nuclear-medicine and dosimetry tools, archaeology and geology dating, and pharmacokinetics and science apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is exponential decay; for the ideal gas law use a gas-law API and for the chemical elements use an elements API.

Uptime

100.0%

Latency

75ms

Subs

4,792

Queueing-theory maths as an API, computed locally and deterministically. The littles-law endpoint applies Little's law, L = λ·W — the average number in a system equals the arrival rate times the average time in the system — and solves for whichever of the three you leave out; it holds for any stable system, from a checkout line to a request pipeline. The mm1 endpoint gives the full steady-state metrics of a single-server M/M/1 queue from the arrival rate λ and the service rate μ: the utilization ρ = λ/μ, the average number in the system and in the queue, the average time in the system and waiting, and the probability the system is empty — and it flags an unstable queue when ρ ≥ 1. The mmc endpoint extends this to a multi-server M/M/c queue with the Erlang-C waiting probability, returning the offered load in erlangs, the per-server utilization, the chance an arrival has to wait, and the same length and time metrics. Rates must share a time unit, and the times come out in that unit. Everything is computed locally and deterministically, so it is instant and private. Ideal for capacity-planning and operations tools, call-centre and staffing apps, server and throughput sizing, and operations-research education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is queueing theory; for descriptive statistics on a list of numbers use a statistics API.

Uptime

100.0%

Latency

81ms

Subs

3,808

Power-screw (lead-screw and screw-jack) mechanics as an API, computed locally and deterministically. The torque endpoint computes the torque to raise and to lower a load on a power screw from the load, the mean thread diameter, the lead (given directly or as pitch × starts) and the coefficient of friction: T_raise = (W·dm/2)·(L + π·μ′·dm)/(π·dm − μ′·L), with the matching lower torque, the lead angle, the efficiency (W·L ÷ 2π·T_raise) and whether the screw is self-locking (it is when the effective friction is at least the tangent of the lead angle). Square threads are the default; pass a thread angle (for example 29° for an ACME thread) and it applies the effective friction μ/cos(half-angle). The effort endpoint turns that torque into the hand force on a lever or handle and the resulting mechanical advantage. The travel endpoint relates turns, lift distance and — with an rpm — the linear speed and time. Lengths are in millimetres, load in newtons and torque in newton-metres. Everything is computed locally and deterministically, so it is instant and private. Thread friction only — add collar/thrust friction separately. Ideal for machine-design and mechanism tools, jack, press, vice and clamp design, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is power-screw mechanics; for the geometry of a screw thread use a thread API and for bolt tightening torque use a torque API.

Uptime

100.0%

Latency

72ms

Subs

4,613

Weld design maths as an API, computed locally and deterministically. The fillet endpoint sizes an equal-leg fillet weld: from the leg size, the weld length and an allowable shear stress it returns the effective throat (leg ÷ √2), the effective area, the load capacity and the strength per millimetre of weld; give a design force instead of a leg and it returns the required throat and leg size, and if you also pass a provided leg it reports the utilization and whether the weld is adequate. The butt endpoint handles a full-penetration butt (groove) weld, where the effective throat equals the plate thickness, returning the area and capacity. The throat endpoint converts between leg and throat — equal-leg (throat = leg ÷ √2), unequal legs (throat = a·b ÷ √(a²+b²)) and throat back to leg. Lengths are in millimetres, stress in megapascals and force in newtons. Everything is computed locally and deterministically, so it is instant and private. An estimating aid, not a code-stamped design — use the allowable stress and electrode from your governing code (AISC, Eurocode). Ideal for structural and fabrication tools, weld-design and estimating apps, maker and metalwork projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is weld strength sizing; for bolt tightening torque use a torque API and for the weight of the steel use a metal-weight API.

Uptime

100.0%

Latency

79ms

Subs

4,699

Catenary (hanging-cable) maths as an API, computed locally and deterministically. The sag endpoint solves the exact catenary for a cable hung between two level supports: from the span, the weight per unit length and either the horizontal tension or the sag, it returns the catenary parameter a = H/w, the sag a·(cosh(L/2a) − 1), the cable length 2a·sinh(L/2a), the minimum tension (the horizontal tension at the lowest point) and the maximum tension at the supports (H·cosh(L/2a)), plus the slack over the straight span. The parabolic endpoint gives the shallow-sag parabolic approximation — sag = w·L²/(8·H) — that is standard for overhead utility lines, and converts between sag and tension either way. The length endpoint returns the cable length for a given span and sag, with the parabolic value alongside for comparison. Forces and lengths are unit-agnostic but must be consistent (for example newtons, newtons per metre and metres). Everything is computed locally and deterministically, so it is instant and private. Ideal for power-line and transmission tools, zip-line and rigging apps, suspension and surveying calculators, and physics and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is hanging-cable catenary maths; for rigging working load limits use a rigging API and for beam deflection use a beam API.

Uptime

100.0%

Latency

79ms

Subs

4,761

Fluid-statics maths as an API, computed locally and deterministically. The pressure endpoint computes the pressure at a depth in a fluid — the gauge pressure ρ·g·h and the absolute pressure (gauge plus atmospheric) — in pascals, kilopascals, bar, psi and atmospheres, for water, seawater, oil, mercury and more, or a custom density; depths accept metres, feet or centimetres, which makes it handy for diving (about 10 m of seawater adds one atmosphere). The force endpoint computes the resultant hydrostatic force on a submerged vertical rectangular surface — an aquarium wall, a tank side, a dam face or a flood gate — as F = ρ·g·h_c·A from its width and the top and bottom depths, and gives the depth of the centre of pressure, which sits below the centroid. The buoyancy endpoint applies Archimedes' principle, F_b = ρ_fluid·g·V, to give the buoyant force and the displaced mass, and — if you supply the object's density or mass — tells you whether it floats or sinks and what fraction sits below the waterline. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil and marine engineering tools, diving and aquarium apps, tank and dam design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fluid statics; for pump power and head use a pump API and for pipe flow rate use a pipe-flow API.

Uptime

100.0%

Latency

78ms

Subs

3,892

Sheet-metal bending maths as an API, computed locally and deterministically. The bend-allowance endpoint computes the bend allowance, bend deduction and outside setback for a single bend from the material thickness, the inside bend radius, the bend angle and the K-factor: the bend allowance is BA = θ·(r + K·t), the outside setback is OSSB = (r + t)·tan(θ/2) and the bend deduction is BD = 2·OSSB − BA, with the neutral-axis position reported too. The flat-length endpoint computes the flat blank length you need to cut: from a list of outside (mold-line) flange lengths, or two flanges, or a total, it subtracts the bend deduction for each bend. The kfactor endpoint lists typical K-factors by material — aluminium around 0.33, mild steel 0.44, stainless 0.45 — and estimates a K-factor from the inside-radius-to-thickness ratio. The K-factor can be given directly or chosen by material, and if the inside radius is omitted it defaults to the thickness. Lengths are unit-agnostic — the output matches whatever unit you supply. Everything is computed locally and deterministically, so it is instant and private. Ideal for sheet-metal CAD/CAM and press-brake tools, fabrication and unfolding apps, maker and prototyping projects, and manufacturing calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is sheet-metal bend development; for the weight of the blank use a metal-weight API.

Uptime

100.0%

Latency

78ms

Subs

4,393

Helical compression-spring maths as an API, computed locally and deterministically. The rate endpoint computes the spring rate from the wire diameter, the mean coil diameter and the number of active coils using k = G·d⁴/(8·D³·n), where the shear modulus G is taken from the material (music wire and spring steel, stainless, phosphor bronze, beryllium copper, titanium and more) or supplied directly — and it reports the rate in newtons per millimetre, newtons per metre and pounds per inch, along with the spring index C = D/d. The force endpoint relates force and deflection through F = k·x in both directions, taking the rate directly or deriving it from the geometry. The stress endpoint computes the shear stress in the wire, τ = 8·F·D·Kw/(π·d³), applying the Wahl correction factor Kw = (4C−1)/(4C−4) + 0.615/C for curvature and direct shear, and also reports the uncorrected stress. Lengths are in millimetres, force in newtons and stress in megapascals. Everything is computed locally and deterministically, so it is instant and private. A design aid — keep the spring index between about 4 and 12 and confirm against the material's allowable stress. Ideal for mechanical-design and CAD tools, spring-selection and prototyping apps, maker and robotics projects, and engineering calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is helical-spring design; for beam deflection use a beam API.

Uptime

100.0%

Latency

79ms

Subs

3,106