16 formulas
Physics Formula Sheet
These are the formulas an introductory physics course uses: motion, forces, momentum, work and energy, circular motion, waves, and electric circuits.
Each formula shows what its letters stand for and their units. Open any one for a worked example and a calculator, or print the sheet to use on homework.
Motion
Distance = Rate × Time
Distance traveled equals speed (rate) times time, the basis of motion word problems.
- How fast, e.g. miles per hour
- How long, in matching time units
Velocity-Time Equation
Calculates final velocity given initial velocity, acceleration, and time.
- Velocity at time t (m/s)
- Starting velocity (m/s)
- Constant acceleration (m/s²)
- Elapsed time (s)
Displacement Equation
Calculates displacement given initial velocity, acceleration, and time.
- Distance traveled (m)
- Starting velocity (m/s)
- Constant acceleration (m/s²)
- Elapsed time (s)
Forces
Newton's Second Law
Force equals mass times acceleration, the foundation of classical mechanics.
- Net force applied to the object (N (Newtons))
- Mass of the object (kg)
- Rate of change of velocity (m/s²)
Newton's Law of Universal Gravitation
Gravitational force between two masses.
- Force of attraction (N)
- ≈ 6.674 × 10⁻¹¹ (N·m²/kg²)
- First mass (kg)
- Second mass (kg)
- Distance between centers (m)
Momentum
Momentum
Product of mass and velocity.
- Quantity of motion (kg·m/s)
- Mass of the object (kg)
- Velocity of the object (m/s)
Impulse
Change in momentum equals impulse.
- Change in momentum (N·s)
- Applied force (N)
- Time interval (s)
- Momentum change (kg·m/s)
Work, energy and power
Work Formula
Work equals force times displacement times the cosine of the angle between them.
- Energy transferred by the force (J (Joules))
- Applied force (N)
- Distance moved (m)
- Angle between force and displacement (degrees)
Kinetic Energy
Energy of motion depends on mass and velocity squared.
- Energy of motion (J (Joules))
- Mass of the object (kg)
- Speed of the object (m/s)
Gravitational Potential Energy
Energy stored due to height in a gravitational field.
- Stored energy (J (Joules))
- Mass of the object (kg)
- Gravitational acceleration ≈ 9.8 (m/s²)
- Height above reference point (m)
Power
Rate of doing work or energy transfer.
- Rate of energy transfer (W (Watts))
- Work done (J)
- Time interval (s)
- Applied force (N)
- Velocity (m/s)
Circular motion
Centripetal Acceleration
Acceleration toward the center of circular motion.
- Acceleration toward center (m/s²)
- Tangential velocity (m/s)
- Radius of circular path (m)
Centripetal Force
Force required to keep an object moving in a circle.
- Force toward center (N)
- Mass of the object (kg)
- Tangential velocity (m/s)
- Radius of circular path (m)
Waves
Wave Speed
Wave speed equals frequency times wavelength.
- Speed of the wave (m/s)
- Frequency of the wave (Hz)
- Distance between wave crests (m)
Frequency-Period Relationship
Frequency is the reciprocal of period.
- Cycles per second (Hz)
- Time for one complete cycle (s)
Electricity
Ohm's Law
Voltage equals current times resistance in an electrical circuit.
- Electric potential difference (V (Volts))
- Flow of electric charge (A (Amps))
- Opposition to current flow (Ω (Ohms))