Physics Calculators
Density
ρ = m / V
Density from mass and volume, or its inverse for any material.
Calculate →Force Equation
F = m · a
Newton's second law — force, mass, and acceleration.
Calculate →Static Friction
F_s ≤ μ_s · N
Maximum static friction force from coefficient and normal force.
Calculate →Kinetic Friction
F_k = μ_k · N
Kinetic friction force from kinetic coefficient and normal force.
Calculate →Circular Motion
v = ω · r · a_c = v² / r
Tangential velocity, centripetal acceleration, and centripetal force in circular motion.
Calculate →Tangential Velocity
v = ω · r = 2πr / T
Tangential (linear) speed of a particle moving along a circular path.
Calculate →Centripetal Acceleration
a_c = v² / r = ω² · r
Center-directed acceleration of an object moving in a circular path.
Calculate →Centripetal Force
F_c = m · v² / r
Inward force required to keep a body in circular motion.
Calculate →Orbital Period
T² = (4π² / GM) · a³
Orbital period from semi-major axis via Kepler's third law.
Calculate →Constant Acceleration Motion
v = v₀ + a · t · x = v₀·t + ½at²
Kinematic equations for one-dimensional motion under constant acceleration.
Calculate →Coulomb's Law
F = k · |q₁ · q₂| / r²
Electrostatic force between two point charges.
Calculate →Doppler Effect Equations
f' = f · (c ± v_o) / (c ∓ v_s)
Frequency shift for a moving source or receiver in the Doppler effect.
Calculate →Einstein Equation
E = m · c²
Mass-energy equivalence for any rest mass.
Calculate →Escape Velocity
v_e = √(2GM / r)
Minimum velocity to escape the gravitational pull of a planet or star.
Calculate →Gravitational Acceleration
g = G · M / r²
Gravitational acceleration at the surface of any planet or moon.
Calculate →Gravitational Force
F = G · m₁ · m₂ / r²
Gravitational force between two masses (Newton's law of universal gravitation).
Calculate →Gravity Equations
g = G · M / r² · F = G · m₁m₂ / r²
Gravitational acceleration, force, and Kepler's third law equations bundle.
Calculate →Hooke's Law
F = −k · x
Spring restoring force and potential energy for a Hookean spring.
Calculate →Impulse Momentum Equations
J = Δp = F · Δt
Impulse, momentum, and the impulse-momentum theorem.
Calculate →Impulse Force
F = Δp / Δt
Average force from change in momentum and contact time.
Calculate →Momentum
p = m · v
Linear momentum from mass and velocity.
Calculate →Impulse-Momentum Theorem
F · Δt = Δp = m · Δv
Connect average force × contact time to the change in linear momentum.
Calculate →Kepler's Third Law
T² / a³ = 4π² / GM
Orbital period and semi-major axis relationship for any two-body system.
Calculate →Kinetic Energy
KE = ½ · m · v²
Translational kinetic energy from mass and velocity.
Calculate →Lens & Mirror Equation
1/f = 1/do + 1/di
Thin lens and mirror equation for object distance, image distance, and focal length.
Calculate →Moment Equation
M = F · d
Moment of force about a pivot point — solve for force, distance, or moment.
Calculate →Newton's Second Law Equations
F_net = m · a
Net force, mass, and acceleration via Newton's second law of motion.
Calculate →Pendulum Formulas
T = 2π · √(L / g) (simple)
Simple and physical pendulum period, length, and moment of inertia equations bundle.
Calculate →Pendulum Period
T = 2π · √(L / g)
Period of a simple pendulum from length and gravitational acceleration.
Calculate →Pendulum Length
L = g · T² / (4π²)
Pendulum length required for a target period.
Calculate →Potential Energy
PE = m · g · h
Gravitational potential energy from mass, height, and gravitational acceleration.
Calculate →Power
P = W / t = F · v
Power from work over time or from force and velocity.
Calculate →Power from Work
P = W / t
Power as work done per unit time.
Calculate →Power from Force and Velocity
P = F · v
Instantaneous power from force and the velocity of its application.
Calculate →Projectile Motion
Range = v₀² · sin(2θ) / g
Range, max height, time of flight, and horizontal/vertical components of projectile motion.
Calculate →Radioactive Material
N = N₀ · e^(−λt)
Number of remaining nuclei, activity, and mass for radioactive decay.
Calculate →Half-Life
t_½ = ln(2) / λ
Half-life of a radioactive isotope from its decay constant.
Calculate →Radioactive Decay
N(t) = N₀ · e^(−λt)
Remaining quantity of a radioactive isotope after a given decay time.
Calculate →Radioactive Activity
A = λ · N = A₀ · e^(−λt)
Decay activity (Becquerels or curies) for a radioactive sample.
Calculate →Mean Lifetime
τ = 1 / λ = t_½ / ln(2)
Mean lifetime of a radioactive nucleus from decay constant or half-life.
Calculate →Snell's Law
n₁ · sin(θ₁) = n₂ · sin(θ₂)
Refraction of light at the boundary between two transparent media.
Calculate →Sound Wave Equations
I = P / A · SPL = 10·log₁₀(I/I₀)
Sound intensity, sound pressure level, and distance attenuation equations bundle.
Calculate →Sound Wave Speed
v = f · λ
Sound wave speed from frequency and wavelength.
Calculate →Sound Intensity Decibels
β = 10 · log₁₀(I / I₀)
Sound intensity level in decibels from measured and reference intensity.
Calculate →Specific Gravity
SG = ρ / ρ_water
Specific gravity from density relative to water.
Calculate →Specific Volume
v = V / m = 1 / ρ
Specific volume from total volume and mass, or density inverse.
Calculate →Stokes Law
v_t = 2(ρ_p − ρ) · g · r² / (9 · μ)
Terminal velocity of a small sphere settling through a viscous fluid.
Calculate →Stress Strain
σ = F / A · ε = ΔL / L · E = σ/ε
Stress, strain, and Young's modulus from force, area, and length change.
Calculate →Torque
τ = r × F = I · α
Torque from force times lever arm, or moment of inertia times angular acceleration.
Calculate →Wavelength, Frequency & Period
v = f · λ · T = 1 / f
Convert between wavelength, frequency, period, and wave speed.
Calculate →Weight Equation
W = m · g
Weight from mass and gravitational acceleration (Earth or other planet).
Calculate →Wien's Equations
λ_max · T = 2.898 × 10⁻³ m·K
Peak emission wavelength of a blackbody at a given temperature (Wien's displacement law).
Calculate →Wing Lift Equations
L = ½ · ρ · v² · S · C_L
Aerodynamic lift from air density, velocity, wing area, and lift coefficient.
Calculate →Work
W = F · d · cos(θ)
Mechanical work done by a force over a distance.
Calculate →Physics calculators covering classical mechanics (motion, force, energy, momentum), electromagnetism (Coulomb's law, Ohm's law, capacitors), waves (Doppler effect, sound), optics (lens/mirror equation, Snell's law), and gravitation (orbital mechanics, escape velocity).
When to use these calculators
Use these for physics homework, engineering pre-screening calculations, lab work, and cross-checks against experimental measurements. Each calculator solves for any variable in its equation and shows the substituted arithmetic step-by-step.
Frequently Asked Questions
- How does the calculator show its work?
- Each calculator displays the substituted arithmetic step-by-step below the solution, so the user can verify the math by hand if needed. The 'Copy result' button captures the full formula → substitution → answer block.
- Are the formulas cross-verified?
- Every calculator's math has been cross-verified against textbook references and round-trip consistency tests (solve A from B, then solve B from A — the result must match the input). Spot-checks against Wolfram Alpha confirm the precision.
- How do I switch between solving for different variables?
- Most calculators in this category support multiple solve-for modes. Pick the unknown variable from the pill-toggle (or equation-card group) above the input fields, then enter the known values. The calculator auto-computes as you type.