# UsePhysics

> Physics for everyday life: free calculators that show the formula and units behind every answer, a CODATA 2022 constants reference with NIST as the cited source, and an open dataset of appliance running costs by country.

Every calculator result is computed from the formula shown on its page. A solved state is linkable: /calculators/<slug>?<input>=<value> restores the inputs and the answer.

## For AI agents (MCP)
- MCP server (Streamable HTTP): https://usephysics.com/api/mcp — tools: list_calculators, calculate, get_constant, list_constants. Every answer carries its formula, units and page URL.

## Calculators
- [Newton's Second Law Calculator (F = ma)](https://usephysics.com/calculators/newtons-second-law): F = m × a
- [Acceleration Calculator (a = Δv / t)](https://usephysics.com/calculators/acceleration): a = (v₁ − v₀) / t
- [Momentum Calculator (p = mv)](https://usephysics.com/calculators/momentum): p = m × v
- [Projectile Motion Calculator (Range, Height, Flight Time)](https://usephysics.com/calculators/projectile-motion): R = v₀² · sin(2θ) / g
- [Free Fall Calculator — Distance, Time & Falling Speed](https://usephysics.com/calculators/free-fall): t = √(2h/g),  v = √(2gh)
- [Free Fall From Time Calculator — Distance and Speed After t Seconds](https://usephysics.com/calculators/free-fall-from-time): d = ½·g·t²,  v = g·t
- [Torque Calculator (τ = r·F·sin θ)](https://usephysics.com/calculators/torque): τ = r × F × sin(θ)
- [Terminal Velocity Calculator](https://usephysics.com/calculators/terminal-velocity): v = √(2mg / (ρ·A·Cd))
- [Tension Calculator (Rope & Cable Tension, T = m(g + a))](https://usephysics.com/calculators/tension): T = m × (g + a)
- [Atwood Machine Calculator (Acceleration & Tension)](https://usephysics.com/calculators/atwood-machine): a = (m₁ − m₂)g / (m₁ + m₂),  T = 2·m₁·m₂·g / (m₁ + m₂)
- [Incline Tension Calculator (Block on a Ramp)](https://usephysics.com/calculators/incline-tension): T = m·g·(sin θ + μ·cos θ)
- [Hanging Mass Tension Calculator (Two Ropes at an Angle)](https://usephysics.com/calculators/hanging-mass-two-ropes): T = m·g / (2·sin θ)
- [Impact Force Calculator (F = ½mv² / d)](https://usephysics.com/calculators/impact-force): F = m·v² / (2·d)
- [Horizontal Projectile Calculator (Range from Height)](https://usephysics.com/calculators/horizontal-projectile): R = v·√(2h/g)
- [Kinetic Energy Calculator — Joules (KE = ½mv²)](https://usephysics.com/calculators/kinetic-energy): KE = ½ × m × v²
- [Potential Energy Calculator (PE = mgh)](https://usephysics.com/calculators/potential-energy): PE = m × g × h
- [Work Calculator (W = F·d·cos θ)](https://usephysics.com/calculators/work): W = F × d × cos(θ)
- [Power Calculator (P = W / t)](https://usephysics.com/calculators/power): P = W / t
- [Watts to Joules Calculator (E = P × t)](https://usephysics.com/calculators/joules-from-watts): E = P × t
- [Ohm's Law Calculator (V = IR)](https://usephysics.com/calculators/ohms-law): I = V / R,  P = V² / R
- [Wavelength Calculator (λ = v / f)](https://usephysics.com/calculators/wavelength): λ = v / f
- [Lens Equation Calculator (Thin Lens: 1/f = 1/dₒ + 1/dᵢ)](https://usephysics.com/calculators/lens-equation): 1/f = 1/dₒ + 1/dᵢ
- [Pressure Calculator (P = F / A)](https://usephysics.com/calculators/pressure): P = F / A
- [Watts to Amps Calculator (I = P / V)](https://usephysics.com/calculators/watts-to-amps): I = P / V
- [Density Calculator (ρ = m / V)](https://usephysics.com/calculators/density): ρ = m / V
- [Specific Heat Calculator (Q = m·c·ΔT)](https://usephysics.com/calculators/specific-heat): Q = m × c × ΔT
- [Thermal Expansion Calculator (Linear, ΔL = α·L₀·ΔT)](https://usephysics.com/calculators/thermal-expansion): ΔL = α × L₀ × ΔT
- [Ideal Gas Law Calculator (PV = nRT)](https://usephysics.com/calculators/ideal-gas-law): P = n·R·T / V
- [Snell's Law Calculator (Refraction Angle)](https://usephysics.com/calculators/snells-law): n₁ · sin(θ₁) = n₂ · sin(θ₂)
- [Hooke's Law Calculator (Spring Force, F = k·x)](https://usephysics.com/calculators/hookes-law): F = k × x
- [Electricity Cost Calculator (Appliance Running Cost)](https://usephysics.com/calculators/electricity-cost): Cost = (W / 1000) × hours × price per kWh

## Data
- [Appliance running costs by country](https://usephysics.com/data/appliance-running-costs): 22 appliances × 29 countries, Eurostat nrg_pc_204 household prices (2025-S2). CC BY 4.0. CSV: https://usephysics.com/data/appliance-running-costs.csv · JSON: https://usephysics.com/data/appliance-running-costs.json

## Physical constants
- [Constants and formula sheet](https://usephysics.com/reference): values from NIST, Fundamental Physical Constants — Complete Listing (2022 CODATA adjustment) (https://physics.nist.gov/cuu/Constants/). Cite NIST for the values.
- [Caesium-133 hyperfine transition frequency (ΔνCs)](https://usephysics.com/reference/caesium-hyperfine-frequency)
- [Speed of light in vacuum (c)](https://usephysics.com/reference/speed-of-light)
- [Planck constant (h)](https://usephysics.com/reference/planck-constant)
- [Elementary charge (e)](https://usephysics.com/reference/elementary-charge)
- [Boltzmann constant (k)](https://usephysics.com/reference/boltzmann-constant)
- [Avogadro constant (NA)](https://usephysics.com/reference/avogadro-constant)
- [Luminous efficacy of 540 THz radiation (Kcd)](https://usephysics.com/reference/luminous-efficacy)
- [Reduced Planck constant (ℏ)](https://usephysics.com/reference/reduced-planck-constant)
- [Newtonian constant of gravitation (G)](https://usephysics.com/reference/gravitational-constant)
- [Standard acceleration of gravity (gn)](https://usephysics.com/reference/standard-gravity)
- [Vacuum electric permittivity (ε₀)](https://usephysics.com/reference/vacuum-electric-permittivity)
- [Vacuum magnetic permeability (μ₀)](https://usephysics.com/reference/vacuum-magnetic-permeability)
- [Characteristic impedance of vacuum (Z₀)](https://usephysics.com/reference/impedance-of-vacuum)
- [Fine-structure constant (α)](https://usephysics.com/reference/fine-structure-constant)
- [Inverse fine-structure constant (α⁻¹)](https://usephysics.com/reference/inverse-fine-structure-constant)
- [Rydberg constant (R∞)](https://usephysics.com/reference/rydberg-constant)
- [Bohr radius (a₀)](https://usephysics.com/reference/bohr-radius)
- [Compton wavelength (electron) (λC)](https://usephysics.com/reference/compton-wavelength)
- [Classical electron radius (re)](https://usephysics.com/reference/classical-electron-radius)
- [Bohr magneton (μB)](https://usephysics.com/reference/bohr-magneton)
- [Nuclear magneton (μN)](https://usephysics.com/reference/nuclear-magneton)
- [Electron mass (me)](https://usephysics.com/reference/electron-mass)
- [Proton mass (mp)](https://usephysics.com/reference/proton-mass)
- [Neutron mass (mn)](https://usephysics.com/reference/neutron-mass)
- [Atomic mass constant (unified atomic mass unit) (mu, u)](https://usephysics.com/reference/atomic-mass-constant)
- [Proton-to-electron mass ratio (mp/me)](https://usephysics.com/reference/proton-electron-mass-ratio)
- [Molar gas constant (R)](https://usephysics.com/reference/molar-gas-constant)
- [Faraday constant (F)](https://usephysics.com/reference/faraday-constant)
- [Stefan–Boltzmann constant (σ)](https://usephysics.com/reference/stefan-boltzmann-constant)
- [Wien wavelength displacement law constant (b)](https://usephysics.com/reference/wien-displacement-constant)
- [Molar volume of an ideal gas (273.15 K, 101.325 kPa) (Vm)](https://usephysics.com/reference/molar-volume-ideal-gas)
- [Standard atmosphere (atm)](https://usephysics.com/reference/standard-atmosphere)
- [Standard-state pressure (p°)](https://usephysics.com/reference/standard-state-pressure)
- [Electron volt (eV)](https://usephysics.com/reference/electron-volt)

## Guides
- [Physics at home](https://usephysics.com/guides/physics-at-home)
- [Physics of money](https://usephysics.com/guides/physics-of-money)
- [Physics for business](https://usephysics.com/guides/physics-for-business)
- [How fast you fall](https://usephysics.com/guides/how-fast-do-you-fall)

## Optional
- [About](https://usephysics.com/about)
- [Sitemap](https://usephysics.com/sitemap.xml)