# Physics Calculators

Exact physics formulas for agents: kinematics, projectiles, inclines, collisions, orbits, oscillators, waves, optics, relativity and blackbody radiation.

## How to pay

Machine-payable over x402. USDC on: Base (eip155:8453), Solana (solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp), Polygon (eip155:137), Arbitrum One (eip155:42161).
No accounts. No API keys. No signup. The paying wallet is the account.

## Machine-readable

- OpenAPI: https://physics-calc.x402tookit.com/openapi.json
- x402 manifest: https://physics-calc.x402tookit.com/.well-known/x402
- Catalog (free): https://physics-calc.x402tookit.com/catalog
- Health (free): https://physics-calc.x402tookit.com/health
- Uptime (free): https://physics-calc.x402tookit.com/uptime

## Endpoints (12)

### GET /blackbody — $0.02
Blackbody radiation: Wien peak wavelength and frequency, Stefan-Boltzmann power per area, and total power for an area or sphere.
Params: temperatureK: number, areaM2?: number, radiusM?: number, emissivity?: number
Example: https://physics-calc.x402tookit.com/blackbody?temperatureK=5772&radiusM=695700000

### GET /collision-1d — $0.02
Head-on collision of two masses: velocities after impact, momentum and kinetic energy lost, elastic to perfectly inelastic.
Params: m1: number, v1: number, m2: number, v2: number, restitution?: number
Example: https://physics-calc.x402tookit.com/collision-1d?m1=2&v1=3&m2=1&v2=0&restitution=1

### GET /incline — $0.02
Block on an incline: weight components, normal force, static friction limit, whether it slips, acceleration and slide time.
Params: massKg: number, angleDeg: number, muStatic?: number, muKinetic?: number, lengthM?: number, gravity?: number
Example: https://physics-calc.x402tookit.com/incline?massKg=10&angleDeg=30&muStatic=0.5&muKinetic=0.3&lengthM=5

### GET /kinematics — $0.02
Constant-acceleration motion: give any three of displacement, start speed, end speed, acceleration, time; get the other two.
Params: s?: number, u?: number, v?: number, a?: number, t?: number
Example: https://physics-calc.x402tookit.com/kinematics?u=20&v=0&a=-5

### GET /lens-mirror — $0.02
Thin lens or mirror equation: give two of focal length, object and image distance, get the third plus magnification.
Params: focalLength?: number, objectDistance?: number, imageDistance?: number
Example: https://physics-calc.x402tookit.com/lens-mirror?focalLength=10&objectDistance=30

### GET /orbit — $0.02
Circular orbit speed, escape speed and period at an altitude or radius around the Sun, a planet, the Moon or a custom mass.
Params: body?: string, altitudeKm?: number, orbitRadiusKm?: number, muKm3PerS2?: number
Example: https://physics-calc.x402tookit.com/orbit?body=earth&altitudeKm=400

### GET /oscillator — $0.02
Period and frequency of a simple pendulum (exact for large swings) or a mass on a spring.
Params: type: string, lengthM?: number, amplitudeDeg?: number, massKg?: number, springConstantNPerM?: number, gravity?: number
Example: https://physics-calc.x402tookit.com/oscillator?type=pendulum&lengthM=1&amplitudeDeg=60

### GET /projectile — $0.02
Projectile motion without drag: range, max height, flight time, impact speed and angle from launch speed, angle and height.
Params: speed: number, angleDeg: number, height?: number, gravity?: number, body?: string
Example: https://physics-calc.x402tookit.com/projectile?speed=20&angleDeg=30&height=10

### GET /relativity — $0.02
Special relativity: Lorentz factor, time dilation, length contraction, total and kinetic energy and momentum at a given speed.
Params: beta?: number, speedMS?: number, properTimeS?: number, properLengthM?: number, restMassKg?: number
Example: https://physics-calc.x402tookit.com/relativity?beta=0.8&properTimeS=10&properLengthM=100&restMassKg=1

### GET /snell — $0.02
Snell's law: refracted angle between two media (names or indices), critical angle and total internal reflection check.
Params: n1: string, n2: string, incidentAngleDeg: number
Example: https://physics-calc.x402tookit.com/snell?n1=air&n2=water&incidentAngleDeg=45

### GET /wave-doppler — $0.02
Wave speed, frequency and wavelength, plus the Doppler-shifted frequency for sound (moving source or observer) or light.
Params: frequencyHz: number, wavelengthM?: number, medium?: string, airTempC?: number, sourceSpeedMS?: number, observerSpeedMS?: number, closingSpeedFractionOfC?: number
Example: https://physics-calc.x402tookit.com/wave-doppler?frequencyHz=400&medium=sound&airTempC=20&sourceSpeedMS=30

### GET /work-energy — $0.02
Work (force x distance x cos angle), kinetic and potential energy, and power, with joule, kWh, calorie and horsepower units.
Params: forceN?: number, distanceM?: number, angleDeg?: number, timeS?: number, massKg?: number, speedMS?: number, heightM?: number, gravity?: number
Example: https://physics-calc.x402tookit.com/work-energy?forceN=50&distanceM=10&angleDeg=60&timeS=5

## Terms

Textbook-model calculators computed locally with CODATA 2018 constants, provided as is. Models ignore air drag, friction unless stated, measurement error and real-world complications; results are for study, estimation and screening, not for engineering, safety or navigation decisions.