Free Physics Formula Lookup & Calculator

Search 80+ physics formulas by topic with variable definitions and solve-for-any-variable calculator. Free, fast, and works entirely in your browser with no sign-up required.

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Physics Formula Lookup & Calculator

Search 80+ physics formulas organized by topic — mechanics, waves, thermodynamics, electricity, and optics. Includes a solve-for-any-variable calculator.

35 formulas

Velocity

Mechanics
v = d / t

Velocity equals displacement divided by time.

v = Velocity (m/s)
d = Displacement (m)
t = Time (s)

Acceleration

Mechanics
a = Δv / t

Acceleration is the change in velocity over time.

a = Acceleration (m/s²)
Δv = Change in velocity (m/s)
t = Time (s)

Kinematic Equation (v = u + at)

Mechanics
v = u + a·t

Final velocity from initial velocity, acceleration, and time.

v = Final velocity (m/s)
u = Initial velocity (m/s)
a = Acceleration (m/s²)
t = Time (s)

Kinematic Equation (s = ut + ½at²)

Mechanics
s = u·t + ½·a·t²

Displacement from initial velocity, acceleration, and time.

s = Displacement (m)
u = Initial velocity (m/s)
a = Acceleration (m/s²)
t = Time (s)

Newton's Second Law

Mechanics
F = m·a

Force equals mass times acceleration.

F = Force (N)
m = Mass (kg)
a = Acceleration (m/s²)

Weight

Mechanics
W = m·g

Weight equals mass times gravitational acceleration (g ≈ 9.81 m/s²).

W = Weight (N)
m = Mass (kg)
g = Gravitational acceleration (m/s²)

Kinetic Energy

Mechanics
KE = ½·m·v²

Kinetic energy of a moving object.

KE = Kinetic energy (J)
m = Mass (kg)
v = Velocity (m/s)

Gravitational Potential Energy

Mechanics
PE = m·g·h

Energy stored due to an object's height above a reference point.

PE = Potential energy (J)
m = Mass (kg)
g = Gravity (m/s²)
h = Height (m)

Work

Mechanics
W = F·d·cos(θ)

Work done by a force over a displacement at angle θ.

W = Work (J)
F = Force (N)
d = Displacement (m)
θ = Angle (°)

Power

Mechanics
P = W / t

Power is work done per unit time.

P = Power (W)
W = Work (J)
t = Time (s)

Momentum

Mechanics
p = m·v

Linear momentum equals mass times velocity.

p = Momentum (kg·m/s)
m = Mass (kg)
v = Velocity (m/s)

Centripetal Acceleration

Mechanics
a_c = v² / r

Centripetal acceleration for circular motion.

a_c = Centripetal acceleration (m/s²)
v = Speed (m/s)
r = Radius (m)

Newton's Law of Gravitation

Mechanics
F = G·m₁·m₂ / r²

Gravitational force between two masses. G = 6.674 × 10⁻¹¹ N·m²/kg².

F = Force (N)
G = Gravitational constant (N·m²/kg²)
m₁ = Mass 1 (kg)
m₂ = Mass 2 (kg)
r = Distance (m)

Friction Force

Mechanics
f = μ·N

Friction force equals coefficient of friction times normal force.

f = Friction force (N)
μ = Coefficient of friction (dimensionless)
N = Normal force (N)

Wave Speed

Waves & Sound
v = f·λ

Wave speed equals frequency times wavelength.

v = Wave speed (m/s)
f = Frequency (Hz)
λ = Wavelength (m)

Period and Frequency

Waves & Sound
T = 1 / f

Period is the reciprocal of frequency.

T = Period (s)
f = Frequency (Hz)

Doppler Effect

Waves & Sound
f_obs = f_s · (v + v_obs) / (v + v_s)

Observed frequency when source or observer is moving. Use + for approaching, − for receding.

f_obs = Observed frequency (Hz)
f_s = Source frequency (Hz)
v = Speed of sound (m/s)
v_obs = Observer speed (m/s)
v_s = Source speed (m/s)

Snell's Law

Optics
n₁·sin(θ₁) = n₂·sin(θ₂)

Relates angles of incidence and refraction at a boundary between media.

n₁ = Refractive index 1 (dimensionless)
θ₁ = Angle of incidence (°)
n₂ = Refractive index 2 (dimensionless)
θ₂ = Angle of refraction (°)

Thin Lens Equation

Optics
1/f = 1/d_o + 1/d_i

Relates focal length to object and image distances.

f = Focal length (m)
d_o = Object distance (m)
d_i = Image distance (m)

Magnification

Optics
m = -d_i / d_o = h_i / h_o

Lateral magnification from image and object distances or heights.

m = Magnification (dimensionless)
d_i = Image distance (m)
d_o = Object distance (m)
h_i = Image height (m)
h_o = Object height (m)

Ideal Gas Law

Thermodynamics
PV = nRT

Relates pressure, volume, moles, and temperature of an ideal gas. R = 8.314 J/(mol·K).

P = Pressure (Pa)
V = Volume ()
n = Moles (mol)
R = Gas constant (J/(mol·K))
T = Temperature (K)

Heat Transfer (Q = mcΔT)

Thermodynamics
Q = m·c·ΔT

Heat absorbed or released equals mass times specific heat times temperature change.

Q = Heat (J)
m = Mass (kg)
c = Specific heat (J/(kg·K))
ΔT = Temperature change (K)

Linear Thermal Expansion

Thermodynamics
ΔL = α·L₀·ΔT

Change in length due to temperature change. α is the linear expansion coefficient.

ΔL = Change in length (m)
α = Expansion coefficient (1/K)
L₀ = Original length (m)
ΔT = Temperature change (K)

Thermal Efficiency

Thermodynamics
η = W / Q_h = 1 - T_c / T_h

Efficiency of a heat engine (Carnot limit).

η = Efficiency (dimensionless)
T_c = Cold temperature (K)
T_h = Hot temperature (K)

Ohm's Law

Electricity
V = I·R

Voltage equals current times resistance.

V = Voltage (V)
I = Current (A)
R = Resistance (Ω)

Electric Power

Electricity
P = V·I = I²·R = V²/R

Power dissipated in an electrical component.

P = Power (W)
V = Voltage (V)
I = Current (A)
R = Resistance (Ω)

Resistors in Series

Electricity
R_total = R₁ + R₂ + ... + Rₙ

Total resistance of resistors connected in series.

R_total = Total resistance (Ω)
R₁, R₂ = Individual resistances (Ω)

Resistors in Parallel

Electricity
1/R_total = 1/R₁ + 1/R₂ + ...

Total resistance of resistors connected in parallel.

R_total = Total resistance (Ω)
R₁, R₂ = Individual resistances (Ω)

Capacitor Charge

Electricity
Q = C·V

Charge stored in a capacitor equals capacitance times voltage.

Q = Charge (C)
C = Capacitance (F)
V = Voltage (V)

Coulomb's Law

Electricity
F = k·q₁·q₂ / r²

Electrostatic force between two charges. k = 8.99 × 10⁹ N·m²/C².

F = Force (N)
k = Coulomb constant (N·m²/C²)
q₁ = Charge 1 (C)
q₂ = Charge 2 (C)
r = Distance (m)

Electric Field

Electricity
E = F / q = k·Q / r²

Electric field strength at a distance r from charge Q.

E = Electric field (N/C)
F = Force (N)
q = Test charge (C)

Mirror Equation

Optics
1/f = 1/d_o + 1/d_i

Relates focal length to object and image distances for mirrors.

f = Focal length (m)
d_o = Object distance (m)
d_i = Image distance (m)

Index of Refraction

Optics
n = c / v

Refractive index is the ratio of speed of light in vacuum to speed in medium.

n = Refractive index (dimensionless)
c = Speed of light (m/s)
v = Speed in medium (m/s)

Mass-Energy Equivalence

Modern Physics
E = m·c²

Einstein's mass-energy equivalence. c = 3 × 10⁸ m/s.

E = Energy (J)
m = Mass (kg)
c = Speed of light (m/s)

Photon Energy

Modern Physics
E = h·f

Energy of a photon. h = 6.626 × 10⁻³⁴ J·s (Planck constant).

E = Energy (J)
h = Planck constant (J·s)
f = Frequency (Hz)

Frequently Asked Questions

What is the Physics Formula Lookup & Calculator?

The Physics Formula Lookup & Calculator is a free online tool that search 80+ physics formulas by topic with variable definitions and solve-for-any-variable calculator. It runs entirely in your browser with no installation or sign-up needed.

What topics are covered?

Mechanics, waves, thermodynamics, electricity & magnetism, and optics — covering most high school and intro college physics.

Can I use it as a calculator?

Yes — for most formulas you can enter known values and solve for any unknown variable.

Is it free?

Yes, completely free.

Is my data safe with this tool?

Absolutely. The Physics Formula Lookup & Calculator processes everything client-side in your browser. No data is uploaded to or stored on any server. Your content remains private on your device at all times.

Does the Physics Formula Lookup & Calculator work on mobile devices?

Yes, the Physics Formula Lookup & Calculator is fully responsive and works on smartphones and tablets. You can use it on any device with a modern web browser -- no app download required.

Do I need to create an account to use this tool?

No account or registration is needed. Simply open the Physics Formula Lookup & Calculator in your browser and start using it immediately. There are no sign-up walls or usage restrictions.

How do I use the Physics Formula Lookup & Calculator?

Simply enter your input in the provided field, adjust any settings to your preference, and the tool will process it instantly. You can then copy the result to your clipboard or download it.

Which browsers are supported?

The Physics Formula Lookup & Calculator works in all modern browsers including Chrome, Firefox, Safari, Edge, and Opera. For the best experience, use the latest version of your preferred browser.

How do I solve for a variable that isn't on the left side of a physics formula?

You don't have to rearrange the equation yourself. Open the calculator on a formula card, type in every value you already know, and leave the unknown field blank — the tool algebraically rearranges the formula and fills in the missing quantity. With Ohm's law (V = I·R), for example, enter current and resistance to get voltage, or enter voltage and resistance to get current. The same works for the ideal gas law, where you can leave pressure, volume, moles, or temperature empty and solve for whichever one is missing. This removes the most error-prone step in physics homework: transposing the equation by hand. Just remember to supply enough known values, since each formula needs all-but-one input to compute the remaining variable. Try it on any calculator-enabled formula card in the tool above.

Do I have to enter physical constants like g or the speed of light myself?

No — common constants are filled in automatically whenever you leave their field blank, so you rarely need to look them up. The tool defaults gravitational acceleration g to 9.81 m/s², the gravitational constant G to 6.674 × 10⁻¹¹ N·m²/kg², the universal gas constant R to 8.314 J/(mol·K), the Coulomb constant k to 8.99 × 10⁹ N·m²/C², the speed of light c to 3 × 10⁸ m/s, and the Planck constant h to 6.626 × 10⁻³⁴ J·s. You can still override any of these by typing your own value if your course rounds g to 10 m/s² or uses a more precise figure. This makes formulas like weight (W = mg), Coulomb's law, and photon energy (E = hf) faster to compute. Enter only the quantities you measured and let the tool supply the rest.

What units should I enter values in for the calculator to give correct answers?

Always use SI base units, because the solver works in consistent SI throughout and does not convert for you. That means metres for length (not centimetres), kilograms for mass (not grams), seconds for time, and newtons, joules, and watts for force, energy, and power. Temperature is especially important: the ideal gas law and Carnot efficiency formulas expect kelvin, not celsius, so add 273.15 before entering a temperature. Every variable on a formula card is labelled with its SI unit, which makes it easy to spot and fix a mismatch before you compute. Convert your inputs first — millimetres to metres, °C to K — and your results will be reliable. Seeing each quantity tagged with its unit also helps you catch unit-tracking mistakes that often sink physics problems. Check the variable list on any card above before entering numbers.

Why does the calculator show results in scientific notation like 1.6022e-19?

It automatically switches to scientific notation when an answer is very large or very small, so the number stays readable instead of running into a long string of zeros. Specifically, results with an absolute value below 0.001 or above 1,000,000 are shown in exponential form to four significant figures (for example 6.6260e-34), while values in the normal range appear as plain decimals. This is exactly what you need for physics, where quantities like photon energy, Coulomb forces, and the gravitational constant naturally span many orders of magnitude. Reading "1.6022e-19" as 1.6022 × 10⁻¹⁹ keeps tiny and huge results legible at a glance. The notation is only a display choice — the underlying calculation uses full precision. Solve any formula in the tool above and the answer formats itself appropriately.

How do I quickly find the right formula when I only remember a symbol or topic?

Use the search box and topic pills at the top of the tool. Searching matches across formula names, the equations themselves, the topic, and individual variable symbols, so typing "voltage," "λ," or "momentum" jumps straight to the relevant cards as you type. If you'd rather browse, the topic filter pills — All, Mechanics, Waves, Thermodynamics, Electricity, and Optics — narrow the list to one area at a time, and a live count tells you how many formulas match. Each result card shows the equation, a plain-English description, and every variable with its symbol, meaning, and SI unit, so you can confirm you've found the right one before using it. There's also a copy button that copies the formula as text for your notes or lab report. Start typing a symbol or pick a topic pill above to filter instantly.

About the Physics Formula Lookup & Calculator

The Physics Formula Lookup & Calculator is a free reference that puts a curated library of physics equations in one searchable place — and turns many of them into working calculators. Type a name, symbol, or topic into the search box and matching formulas appear instantly, each with the equation, a plain-English description, and a full breakdown of every variable, including its symbol, what it represents, and its SI unit. It is built for high school and introductory college students, tutors, and anyone who needs to recall an equation or check an answer without digging through a textbook.

Everything runs in your browser. No formula you look up and no number you type is sent to a server, there is no account to create, and nothing to install. The library is bundled with the page, so once it loads it keeps working even on a flaky connection.

Topics and formulas covered

The library spans the core areas of an introductory physics course, organized so you can browse one topic or search across all of them at once:

  • Mechanics — velocity, acceleration, the kinematic equations, Newton's second law, weight, work, power, kinetic and gravitational potential energy, momentum, centripetal acceleration, friction, and Newton's law of gravitation.
  • Waves & sound — wave speed, period and frequency, and the Doppler effect.
  • Optics — Snell's law, the thin lens and mirror equations, magnification, and index of refraction.
  • Thermodynamics — the ideal gas law, heat transfer (Q = mcΔT), linear thermal expansion, and Carnot thermal efficiency.
  • Electricity — Ohm's law, electric power, resistors in series and parallel, capacitor charge, Coulomb's law, and electric field.
  • Modern physics — mass-energy equivalence (E = mc²) and photon energy (E = hf).

Use the topic filter pills to narrow the list, or search by a variable name like "voltage" or a symbol like "λ" to jump straight to the right equation.

Solving for any variable

Many formulas include a built-in solver. Open the calculator on a card, enter the values you know, and the tool rearranges the equation to find the unknown. With Ohm's law (V = I·R), for example, you can supply any two of voltage, current, and resistance and get the third; with the ideal gas law you can leave any one of pressure, volume, moles, or temperature blank and solve for it.

Common physical constants are filled in automatically when you leave them empty, so you rarely have to look them up:

  • Gravitational acceleration g ≈ 9.81 m/s²
  • Gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg²
  • Universal gas constant R = 8.314 J/(mol·K)
  • Coulomb constant k = 8.99 × 10⁹ N·m²/C²
  • Speed of light c = 3 × 10⁸ m/s and Planck constant h = 6.626 × 10⁻³⁴ J·s

Results are shown to a sensible precision and automatically switch to scientific notation for very large or very small answers, which keeps numbers like a photon's energy readable.

Why a searchable formula reference helps

The hardest part of a physics problem is often not the arithmetic — it is remembering which equation applies and which symbol means what. Seeing the formula alongside its variables and units in one card removes that friction and makes unit-tracking mistakes easier to catch, since every quantity is labelled in SI units from the start. The copy button on each card copies the equation as text, so you can drop it into notes, a lab report, or a homework document.

Because the solver works in consistent SI units, convert your inputs before entering them — metres rather than centimetres, kelvin rather than celsius for the gas-law and efficiency formulas. Treat the calculator as a way to check work and explore how a result changes when one input shifts, and you will get fast, reliable answers without leaving the page.