Physics formulas

Mechanics formulas

Calculate motion, acceleration, and forces using clearly described quantities and compatible units.

Formulas and calculators

Calculate average speed, distance travelled, or travel time. The formula can be rearranged for any of the three quantities.

v = s / t

Calculated quantities

v - average speed · s - distance · t - elapsed time

Calculate average acceleration, change in velocity, or elapsed time from motion along one axis.

a = Δv / t

Calculated quantities

a - average acceleration · Δv - change in velocity · t - elapsed time

Calculate net force, mass, or acceleration using the relationship between force and motion.

F = m × a

Calculated quantities

F - net force · m - mass · a - acceleration

v = s / t

When to use it: Average speed equals the distance travelled divided by the elapsed time.
Calculated quantities: v - average speed (m/s) · s - distance (m) · t - elapsed time (s)
Worked example: Average speed of a cyclist: A cyclist travels 36 km in 1.5 hours. Find the average speed.

a = Δv / t

When to use it: Average acceleration is the change in velocity divided by the elapsed time.
Calculated quantities: a - average acceleration (m/s²) · Δv - change in velocity (m/s) · t - elapsed time (s)
Worked example: Car accelerating from rest: A car changes its velocity by 20 m/s in 5 s. Find its average acceleration.

F = m × a

When to use it: The net external force on a system equals its mass multiplied by its acceleration.
Calculated quantities: F - net force (N) · m - mass (kg) · a - acceleration (m/s²)
Worked example: Net force accelerating a car: A 1200 kg car accelerates at 2.5 m/s². Find the net force.

The result v is average scalar speed over the stated interval. For uniform motion it is also the speed at every instant.
Distance s is the length of the travelled path, not vector displacement.
Elapsed time t must be greater than zero, and speed cannot be negative in this scalar model.
All values must use compatible units; convert minutes to hours or seconds before calculating when necessary.
The formula returns average acceleration over the stated time interval, not acceleration at a single instant.
Velocity change and acceleration are signed components along one chosen axis; a negative result indicates the opposite direction.
Elapsed time must be greater than zero. Acceleration must also be non-zero when it is used to calculate time.
Input units must be compatible and are converted before calculation.

Mixing kilometres with metres or hours with seconds without converting them.
Writing 1 hour 30 minutes as 1.30 h instead of 1.5 h.
Treating average speed as the highest or instantaneous speed during a changing journey.
Confusing distance travelled with displacement between the start and end points.
Using final velocity instead of the change between final and initial velocity.
Treating a negative acceleration component as an invalid result.
Mixing km/h with seconds without conversion.
Calling the result instantaneous acceleration when only an interval is known.