Kinematics Calculator

Solve one-dimensional constant-acceleration motion from displacement, velocity, acceleration, and time with the equation used shown.

At a glance

Computes
Constant-acceleration motion in one dimension, solved for any missing quantity.
You supply
Any three of displacement, initial velocity, final velocity, acceleration, and time.
Use when
Acceleration is constant and the motion is along one straight line.
Not for
Motion in two dimensions under gravity, such as a launched projectile. Projectile Motion Calculator
Unit system

Signed direction.

Signed direction.

Signed direction.

Signed direction.

Seconds.

Position against Time

0.00.51.01.52.005101520Position

Velocity against Time

0.00.51.01.52.005101520Velocity

Acceleration against Time

0.00.51.01.52.068101214Acceleration
All values are 10; the axis is drawn over a nominal range around it.

Kinematics result

Enter any three values

Constant acceleration in one dimension.

Motion variables
VariableValueUnitStatus
Export

v = v0 + a t; dx = v0 t + 0.5 a t^2; v^2 = v0^2 + 2 a dx How?

How this is calculated

The solver uses the standard one-dimensional constant-acceleration equations. Extra supplied values are checked against the same equations.

Formula: v = v0 + a t; dx = v0 t + 0.5 a t^2; v^2 = v0^2 + 2 a dx

The SUVAT equations

SUVAT names the five quantities in straight-line motion under constant acceleration: displacement, initial velocity, final velocity, acceleration, and time. Each equation omits one quantity, so the missing value determines which equation is useful. This page writes displacement as dx and initial velocity as v0, then names the equation used under every result.

  • v = v0 + a t leaves out displacement.
  • dx = v0 t + 0.5 a t^2 leaves out final velocity.
  • v^2 = v0^2 + 2 a dx leaves out time.
  • dx = ((v0 + v) / 2) t leaves out acceleration.

Signs carry direction. Choose one direction as positive and keep that convention for every value. Negative acceleration does not automatically mean slowing down: an object moving in the negative direction under negative acceleration is speeding up.

Free fall

Free fall is the vertical case with acceleration fixed at standard gravity. The preset loads a starting velocity of zero and 9.80665 metres per second squared downward, or 32.174049 feet per second squared in US customary units. Supply the fall time or signed drop height and the same SUVAT solver fills in the rest. A three-second drop from rest moves 44.129925 metres downward and reaches 29.41995 metres per second downward.

The model omits air resistance, so it is best for a dense object over a short distance. For motion with a horizontal component, use the projectile motion calculator. Its vertical calculation follows the same signed convention.

Sources

  1. OpenStax College Physics 2e, Motion Equations for Constant Acceleration in One Dimension. OpenStax. Retrieved .

Method last reviewed