Physics Calculators

Calculate force, mass, or acceleration using F = ma

F = ma

Calculate final velocity using v = u + at

v = u + at

Calculate displacement using s = ut + ½at²

s = ut + ½at²

Calculate using v² = u² + 2as

v² = u² + 2as

Calculate horizontal range of a projectile

R = v²sin(2θ)/g

Complete projectile motion calculation

x = v₀cos(θ)t, y = v₀sin(θ)t - ½gt²

Calculate centripetal force and acceleration

a_c = v²/r, F_c = mv²/r

Calculate angular displacement, velocity, and acceleration

θ = ω₀t + ½αt²

Calculate momentum from mass and velocity

p = mv

Calculate impulse from force and time

J = FΔt = Δp

Calculate final velocities after elastic collision in 1D

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Calculate final velocity after perfectly inelastic collision

m₁u₁ + m₂u₂ = (m₁ + m₂)v

Calculate work done by a force

W = Fd cos(θ)

Calculate kinetic energy

KE = ½mv²

Calculate GPE = mgh

GPE = mgh

Calculate energy stored in a spring

EPE = ½kx²

Calculate total mechanical energy (KE + PE)

E = KE + GPE

Calculate power from work and time

P = W/t

Calculate power using P = Fv

P = Fv

Calculate efficiency from useful and total energy

η = E_useful/E_total × 100%

Calculate weight from mass and gravity

W = mg

Calculate maximum static friction force

f_s ≤ μ_sN

Calculate kinetic friction force

f_k = μ_kN

Calculate spring force from displacement

F = -kx

Calculate torque from force and lever arm

τ = rF sin(θ)

Calculate moment of inertia for a point mass

I = mr²

Calculate rotational kinetic energy

KE_rot = ½Iω²

Calculate angular momentum

L = Iω

Calculate gravitational force between two masses using Newton's law

F = Gm₁m₂/r²

Calculate gravitational force (big masses like planets)

F = GMm/r²

Calculate forces on an inclined plane

F_parallel = mg sin(θ), F_normal = mg cos(θ)

Calculate acceleration and tension in an Atwood machine

a = (m₁ - m₂)g/(m₁ + m₂)

Calculate mechanical advantage of pulley systems

MA = number of supporting ropes

Calculate force and mechanical advantage of a lever

F₁d₁ = F₂d₂

Calculate pressure from force and area

P = F/A

Calculate density from mass and volume

ρ = m/V

Calculate pressure, volume, temperature, or moles using PV = nRT

PV = nRT

Calculate moles from P, V, T

n = PV/RT

Calculate pressure-volume relationship at constant temperature

P₁V₁ = P₂V₂

Calculate volume-temperature relationship at constant pressure

V₁/T₁ = V₂/T₂

Calculate pressure-temperature relationship

P₁/T₁ = P₂/T₂

Calculate using P₁V₁/T₁ = P₂V₂/T₂

P₁V₁/T₁ = P₂V₂/T₂

Calculate change in length due to temperature

ΔL = αL₀ΔT

Calculate change in volume due to temperature

ΔV = βV₀ΔT

Calculate heat energy from mass, specific heat, and temperature change

Q = mcΔT

Calculate specific heat from energy, mass, and temperature change

c = Q/(mΔT)

Calculate energy for phase change

Q = mL

Calculate final temperature when mixing substances

m₁c₁(T_f - T₁) + m₂c₂(T_f - T₂) = 0

Calculate change in internal energy

ΔU = Q - W

Calculate maximum theoretical efficiency of a heat engine

η = 1 - T_c/T_h

Calculate entropy change from heat transfer

ΔS = Q/T

Calculate thermal radiation power

P = εσAT⁴

Calculate cooling temperature over time

T(t) = T_env + (T₀ - T_env)e^(-kt)

Calculate conductive heat transfer rate

Q/t = kA(ΔT)/d

Calculate voltage, current, resistance, or power

V = IR, P = IV

Calculate power from voltage and current

P = IV

Calculate total resistance in series

R_total = R₁ + R₂ + ...

Calculate total resistance in parallel

1/R_total = 1/R₁ + 1/R₂ + ...

Calculate capacitance from charge and voltage

C = Q/V

Calculate total capacitance in series

1/C_total = 1/C₁ + 1/C₂ + ...

Calculate total capacitance in parallel

C_total = C₁ + C₂ + ...

Calculate RC time constant

τ = RC

Calculate voltage across charging capacitor over time

V(t) = V₀(1 - e^(-t/RC))

Calculate voltage across discharging capacitor

V(t) = V₀e^(-t/RC)

Calculate force between two charges

F = kq₁q₂/r²

Calculate electric field from a point charge

E = kq/r²

Calculate electric potential V = kq/r

V = kq/r

Calculate potential energy between two charges

U = kq₁q₂/r

Calculate magnetic field around a current-carrying wire

B = μ₀I/(2πr)

Calculate magnetic field inside a solenoid

B = μ₀nI

Calculate force on a charge in magnetic field

F = qvB sin(θ)

Calculate induced EMF from changing magnetic flux

ε = -N(ΔΦ/Δt)

Calculate inductive time constant

τ = L/R

Calculate inductive reactance

X_L = 2πfL

Calculate capacitive reactance

X_C = 1/(2πfC)

Calculate resonant frequency of an LC circuit

f = 1/(2π√(LC))

Calculate total impedance of series RLC circuit

Z = √(R² + (X_L - X_C)²)

Calculate voltage drops in a simple series circuit

ΣV = 0

Calculate currents at a junction node

ΣI_in = ΣI_out

Calculate unknown resistance in a balanced bridge

R_x = R₃ × R₂/R₁

Calculate output voltage in a voltage divider

V_out = V_in × R₂/(R₁ + R₂)

Calculate the resistor value needed for an LED

R = (V_supply - V_LED) / I_LED

Calculate voltage and turns ratio in a transformer

V_p/V_s = N_p/N_s

Calculate wave speed from frequency and wavelength

v = fλ

Calculate frequency from wave speed and wavelength

f = v/λ

Calculate wavelength from wave speed and frequency

λ = v/f

Calculate wave period from frequency

T = 1/f

Calculate sound intensity level in decibels

β = 10log₁₀(I/I₀)

Calculate observed frequency due to motion

f' = f(v ± vₒ)/(v ∓ vₛ)

Calculate beat frequency from two sound waves

f_beat = |f₁ - f₂|

Calculate resonant frequencies of a fixed string

f_n = nv/(2L)

Calculate resonant frequencies of open/closed pipes

f_n = nv/(2L) (open), f_n = nv/(4L) (closed)

Add sound levels from multiple sources

β_total = 10log₁₀(Σ10^(βᵢ/10))

Calculate how sound intensity changes with distance

I₂ = I₁(r₁/r₂)²

Calculate refraction angle or refractive index

n₁sin(θ₁) = n₂sin(θ₂)

Calculate focal length, image distance, or object distance

1/f = 1/d₀ + 1/dᵢ

Calculate image position and magnification for mirrors

1/f = 1/d₀ + 1/dᵢ, f = R/2

Calculate magnification from image and object sizes

m = hᵢ/h₀ = -dᵢ/d₀

Calculate critical angle for total internal reflection

θ_c = sin⁻¹(n₂/n₁)

Calculate angle for polarized reflection

θ_B = tan⁻¹(n₂/n₁)

Calculate focal length from lens geometry

1/f = (n-1)(1/R₁ - 1/R₂)

Calculate fringe spacing in double-slit experiment

Δy = λL/d

Calculate central maximum width in single-slit diffraction

w = 2λL/a

Calculate X-ray diffraction angle

nλ = 2d sin(θ)

Calculate optical power of a lens

P = 1/f

Calculate expanded beam diameter

D₂ = D₁ × f₂/f₁

Calculate pressure, velocity, or height in a fluid

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

Calculate buoyant force

F_b = ρVg

Calculate volumetric flow rate

Q = Av

Calculate velocity change in a constricted pipe

A₁v₁ = A₂v₂

Predict laminar vs turbulent flow

Re = ρvD/μ

Calculate pressure drop in laminar pipe flow

Q = πΔPr⁴/(8μL)

Calculate force multiplication in hydraulic systems

F₂ = F₁ × A₂/A₁

Calculate velocity from pressure difference

v₂ = √(2(P₁-P₂)/ρ(1-(A₂/A₁)²))

Calculate surface tension force

F = γL

Calculate height of liquid in capillary tube

h = 2γcos(θ)/(ρgr)

Calculate photon energy and kinetic energy of emitted electron

E = hf, KE = hf - φ

Calculate energy from mass using Einstein's formula

E = mc²

Calculate the wavelength of a matter wave

λ = h/p

Calculate minimum uncertainty in position or momentum

ΔxΔp ≥ ħ/2

Calculate time dilation effect

Δt' = Δt/√(1-v²/c²)

Calculate length contraction effect

L = L₀√(1-v²/c²)

Calculate kinetic energy at relativistic speeds

KE = (γ-1)mc²

Calculate blackbody spectral radiance

B(λ,T) = 2hc²/λ⁵ × 1/(e^(hc/λkT)-1)

Calculate peak wavelength of blackbody radiation

λ_max = b/T

Calculate wavelength shift in Compton scattering

Δλ = h/(mₑc)(1-cos(θ))

Calculate remaining quantity after time

N = N₀e^(-λt)

Calculate half-life from decay constant

t₁/₂ = ln(2)/λ

Calculate nuclear binding energy

B = Δm × c²

Calculate age from remaining Carbon-14

t = -ln(N/N₀)/λ

Calculate energy released in fission

E = Δm × 931.5 MeV

Calculate radiation dose equivalent

H = D × Q

Calculate escape velocity from a celestial body

v_esc = √(2GM/r)

Calculate orbital velocity at a given altitude

v_orb = √(GM/r)

Calculate orbital period from semi-major axis

T² = (4π²/GM)a³

Calculate orbital period of a moon

T² = (4π²/GM)a³

Calculate differential tidal force

F_tidal ∝ 2GMmR/r³

Convert between astronomical distance units

1 ly = 9.461e15 m

Calculate your weight on different celestial bodies

W = mg

Calculate habitable zone around a star

d = √(L_star/L_sun) × 1 AU

Calculate absolute magnitude from apparent magnitude and distance

M = m - 5log₁₀(d/10)

Calculate the event horizon radius of a black hole

r_s = 2GM/c²

Calculate star luminosity from temperature and radius

L = 4πR²σT⁴

Calculate speed, distance, or time

s = d/t

Calculate fuel consumption and efficiency

mpg = miles/gallons

Calculate period of a simple pendulum

T = 2π√(L/g)

Calculate frequency of a simple pendulum

f = 1/(2π)√(g/L)

Calculate period and frequency of a mass-spring system

T = 2π√(m/k)

Calculate relative centrifugal force

RCF = 1.118 × r × (RPM/1000)²

Calculate acceleration from velocity change and time

a = Δv/t

Calculate stopping distance from speed and deceleration

d = v²/(2a)

Calculate electricity cost of an appliance

Cost = Power × Time × Rate

Calculate battery life from capacity and load

Time = Capacity / Current

Calculate resistance of a wire from material and dimensions

R = ρL/A

Calculate wire diameter from AWG

d = 0.127 × 92^((36 - AWG)/39)

Estimate monthly electricity bill

Cost = Σ(P_i × t_i × rate)

Convert between imperial and metric units

Conversion factors

Calculate speed of sound in air based on temperature

v = 331.3√(1 + T/273.15)

Calculate Mach number from speed and temperature

M = v/c

Convert between intensity ratio and decibels

dB = 10log₁₀(I/I_ref)

Calculate energy used by multiple appliances

E = ΣP×t

Calculate effective focal length from sensor crop factor

f_eff = f × crop_factor

Calculate depth of field for a camera lens

DOF = 2Nc(1+1/m)/m

Calculate target heart rate for exercise

HR_target = (220 - age) × intensity

Estimate calories burned during physical activity

MET × weight(kg) × hours

Calculate BMI from height and weight

BMI = weight(kg)/height(m)²

Calculate BMR using Mifflin-St Jeor equation

BMR = 10W + 6.25H - 5A ± 161

Calculate recommended daily water intake

Water = weight × 0.033

Calculate final velocities in 2D elastic collision

Conservation of momentum & energy in 2D

Calculate rolling resistance force

F_r = C_r × N

Calculate drag force on an object

F_D = ½ρv²C_DA

Calculate terminal velocity of a falling object

v_t = √(2mg/ρAC_D)

Calculate optimal speed on a banked curve

v = √(rg tan(θ))

Calculate tension at any point in pendulum swing

T = mg cos(θ) + mv²/L

Calculate areal velocity of orbiting body

dA/dt = L/(2m)

Calculate reduced mass of two-body system

μ = m₁m₂/(m₁+m₂)

Calculate coefficient of restitution from bounce heights

e = √(h/h₀)

Calculate efficiency of a heat engine

η = 1 - Q_c/Q_h

Calculate COP of a refrigerator

COP = Q_c/W

Calculate efficiency of an Otto cycle engine

η = 1 - 1/r^(γ-1)

Calculate heat transfer through composite materials

Q/t = ΔT/Σ(R)

Calculate net radiative heat transfer between surfaces

Q = εσA(T₁⁴ - T₂⁴)

Calculate work done in isothermal expansion

W = nRT ln(V₂/V₁)

Calculate electric flux using Gauss's Law

Φ_E = Q/ε₀

Calculate magnetic flux through a loop

Φ = BA cos(θ)

Calculate electric field between parallel plates

E = V/d

Calculate charge on capacitor plates

Q = CV

Calculate capacitance of parallel plates

C = ε₀ε_rA/d

Calculate cyclotron frequency of charged particle

f_c = qB/(2πm)

Calculate Hall voltage across a conductor

V_H = IB/(net)

Calculate energy stored in a capacitor

E = ½CV² = ½QV

Calculate energy stored in an inductor

E = ½LI²

Calculate RMS power in AC circuits

P = V_rms × I_rms × cos(φ)

Decode 4-band resistor color code

R = (digit1×10 + digit2)×multiplier ± tolerance

Calculate intensity of a wave

I = P/A = ½ρω²A²v

Calculate resultant amplitude of two waves

A_resultant = √(A₁² + A₂² + 2A₁A₂cos(Δφ))

Calculate wave speed from tension and linear density

v = √(T/μ)

Calculate SPL from pressure amplitude

SPL = 20log₁₀(p/p_ref)

Calculate energy of lattice vibrations

E = ħω

Simplified projectile motion with linear drag

Includes drag force F = -kv

Calculate friction factor for turbulent pipe flow

Colebrook-White equation

Calculate Mach angle for shock waves

sin(μ) = 1/M

Calculate energy released in fusion reactions

E = Δm × c²

Calculate relativistic Doppler shift for light

λ_obs = λ_src × √((1+β)/(1-β))