How do I use the mini-calculator?

Click any formula card to expand it. Scroll to the Quick Calculator section. Enter values for the variables you know (leave the unknown field blank), select which variable you want to solve for in the dropdown, then click Calculate. The result appears immediately below.

What does the difficulty level mean?

HS (High School / GCSE): standard secondary school physics. College (AP / University): first-year university or AP Physics level. Advanced (Graduate / Research): post-graduate concepts. You can filter by difficulty level using the Level dropdown.

What is the difference between speed and velocity?

Speed is a scalar quantity (magnitude only, e.g., 60 km/h). Velocity is a vector quantity (magnitude AND direction, e.g., 60 km/h northward). Many kinematics formulas use velocity, so direction matters - displacement and acceleration are also vectors.

Why do some formulas show SI units and others show specific values?

SI units are given for variables where you supply the value. For physical constants (like G = 6.674×10⁻¹¹ N·m²/kg², c = 3×10⁸ m/s, h = 6.626×10⁻³⁴ J·s), the value is embedded in the formula calculator so you don't need to enter it separately.

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Physics Formula Sheet

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Total Formulas

Uniform Velocity

s = v · t

HSKinematics

Velocity (constant acceleration)

v = u + at

HSKinematics

Displacement (constant acceleration)

s = ut + ½at²

HSKinematics

Velocity-displacement

v² = u² + 2as

HSKinematics

Projectile Range

R = v₀² sin(2θ) / g

HSKinematics

Projectile Max Height

H = v₀² sin²(θ) / 2g

HSKinematics

Angular Velocity

ω = Δθ / Δt

HSDynamics

Newton's Second Law

F = ma

HSDynamics

Gravitational Force

F = GMm / r²

HSDynamics

Weight

W = mg

HSDynamics

Friction Force

f = μN

HSDynamics

Momentum

p = mv

HSDynamics

Impulse

J = F · Δt = Δp

HSDynamics

Centripetal Force

Fc = mv² / r

HSDynamics

Torque

τ = r × F = rF sin(θ)

HSEnergy & Work

Work Done

W = F · d · cos(θ)

HSEnergy & Work

Kinetic Energy

KE = ½mv²

HSEnergy & Work

Gravitational Potential Energy

PE = mgh

HSEnergy & Work

Power

P = W / t = F · v

HSEnergy & Work

Elastic Potential Energy

PE = ½kx²

HSWaves

Wave Speed

v = fλ

HSWaves

Period & Frequency

T = 1/f

CollegeWaves

Simple Harmonic Motion

x = A cos(ωt + φ)

HSWaves

Doppler Effect (sound)

f′ = f (v ± v_obs) / (v ∓ v_src)

CollegeWaves

String Resonant Frequencies

fₙ = n v / 2L

HSThermodynamics

Ideal Gas Law

PV = nRT

HSThermodynamics

Heat Transfer (conduction)

Q = mcΔT

CollegeThermodynamics

Carnot Efficiency

η = 1 − T_c / T_h

HSThermodynamics

Thermal Expansion (linear)

ΔL = αL₀ΔT

CollegeThermodynamics

First Law of Thermodynamics

ΔU = Q − W

HSElectricity

Ohm's Law

V = IR

HSElectricity

Electric Power

P = IV = I²R = V²/R

HSElectricity

Coulomb's Law

F = kq₁q₂ / r²

HSElectricity

Resistors in Series

R_total = R₁ + R₂ + …

CollegeElectricity

Capacitor Energy

E = ½CV²

CollegeElectricity

Magnetic Force on Moving Charge

F = qvB sin(θ)

CollegeElectricity

Faraday's Law (EMF)

ε = −dΦ/dt = −NΔΦ/Δt

HSOptics

Snell's Law

n₁ sin(θ₁) = n₂ sin(θ₂)

HSOptics

Thin Lens Equation

1/f = 1/dₒ + 1/dᵢ

HSOptics

Photon Energy

E = hf = hc/λ

HSOptics

Mirror Equation

1/f = 1/dₒ + 1/dᵢ

HSModern Physics

Einstein's Mass-Energy

E = mc²

CollegeModern Physics

de Broglie Wavelength

λ = h/mv

CollegeModern Physics

Radioactive Decay

N = N₀ e^(−λt)

CollegeModern Physics

Heisenberg Uncertainty Principle

Δx · Δp ≥ ℏ/2

CollegeModern Physics

Lorentz Time Dilation

Δt′ = γΔt = Δt / √(1 − v²/c²)

Difficulty Levels

HS - High School / GCSECollege - AP / UniversityAdvanced - Graduate / Research

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A comprehensive physics formula reference covering 8 major topics: Kinematics (velocity, acceleration, projectile motion, angular velocity), Dynamics (Newton's laws, gravity, friction, momentum, torque), Energy & Work (work, kinetic energy, potential energy, power, springs), Waves (wave speed, period, SHM, Doppler, resonance), Thermodynamics (ideal gas law, heat transfer, Carnot efficiency), Electricity (Ohm's law, power, Coulomb's law, capacitor energy, Faraday's law), Optics (Snell's law, thin lens, photon energy), and Modern Physics (E=mc², de Broglie wavelength, radioactive decay, Heisenberg uncertainty, time dilation). Each formula card shows the equation, all variable definitions with SI units, usage notes, and an interactive mini-calculator to solve for any unknown variable. Filter by category and difficulty level (High School, College, Advanced). Search by formula name or variable.

How to Use

1Use the search bar to find a formula by name, variable, or topic keyword
2Use the Category dropdown to browse a specific physics topic (e.g. Thermodynamics)
3Click a formula card to expand it and see variable definitions, units, and usage notes
4In the Quick Calculator section, fill in the known values and select the variable to solve for
5Use the Level filter to focus on High School, College, or Advanced formulas

Features

40+ formulas across 8 physics topics
Categories: Kinematics, Dynamics, Energy & Work, Waves, Thermodynamics, Electricity, Optics, Modern Physics
3 difficulty levels: HS (High School), College (AP/University), Advanced
Search by formula name, variable name, or topic keyword
Each formula card shows the equation, all variable definitions with SI units, and usage notes
Built-in mini-calculator: enter known values and solve for any unknown variable
Physical constants (G, c, h, R) pre-embedded in relevant calculators
Copy any formula to clipboard with one click
Expandable cards - keep only what you need open

Physics Formula Sheet

Uniform Velocity

Velocity (constant acceleration)

Displacement (constant acceleration)

Velocity-displacement

Projectile Range

Projectile Max Height

Angular Velocity

Newton's Second Law

Gravitational Force

Weight

Friction Force

Momentum

Impulse

Centripetal Force

Torque

Work Done

Kinetic Energy

Gravitational Potential Energy

Power

Elastic Potential Energy

Wave Speed

Period & Frequency

Simple Harmonic Motion

Doppler Effect (sound)

String Resonant Frequencies

Ideal Gas Law

Heat Transfer (conduction)

Carnot Efficiency

Thermal Expansion (linear)

First Law of Thermodynamics

Ohm's Law

Electric Power

Coulomb's Law

Resistors in Series

Capacitor Energy

Magnetic Force on Moving Charge

Faraday's Law (EMF)

Snell's Law

Thin Lens Equation

Photon Energy

Mirror Equation

Einstein's Mass-Energy

de Broglie Wavelength

Radioactive Decay

Heisenberg Uncertainty Principle

Lorentz Time Dilation

How to Use

Features

Frequently Asked Questions

How do I use the mini-calculator?

What does the difficulty level mean?

What is the difference between speed and velocity?

Why do some formulas show SI units and others show specific values?

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