Displacement Calculator

Our free online displacement calculator helps you find the distance an object moves from its starting point. Whether you know average velocity and time, initial and final velocities, or acceleration and time, this calculator supports three common formulas for physics and engineering problems.

What is Displacement?

Displacement is a vector quantity that refers to the change in position of an object. Unlike distance, which measures the total path length traveled, displacement measures the straight-line distance from the starting point to the ending point, along with the direction.

Displacement Formulas

This calculator supports three common displacement formulas:

1. Average Velocity Formula: s = vt

\[ s = \overline{v}t \]

Use this formula when you know the average velocity and time traveled. This is the simplest form and works for constant velocity motion.

2. Initial and Final Velocity Formula: s = ½(v + u)t

\[ s = \frac{1}{2}(v + u)t \]

Use this formula when you know the initial velocity, final velocity, and time. This applies to uniformly accelerated motion where the average velocity is the mean of initial and final velocities.

3. Acceleration Formula: s = ut + ½at²

\[ s = ut + \frac{1}{2}at^2 \]

Use this formula when you know initial velocity, acceleration, and time. This is the standard kinematic equation for uniformly accelerated motion.

Examples

Example 1: Average Velocity

A car travels at an average speed of 25 m/s for 10 seconds. What is the displacement?

\[ s = 25 \times 10 = 250 \text{ meters} \]

Example 2: Initial and Final Velocity

A car accelerates from 10 m/s to 30 m/s over 10 seconds. What is the displacement?

\[ s = \frac{1}{2}(30 + 10) \times 10 = \frac{1}{2} \times 40 \times 10 = 200 \text{ meters} \]

Example 3: Acceleration

A car starts from rest (u = 0 m/s) and accelerates at 3 m/s² for 5 seconds. What is the displacement?

\[ s = 0 \times 5 + \frac{1}{2} \times 3 \times 5^2 = 0 + \frac{1}{2} \times 3 \times 25 = 37.5 \text{ meters} \]

Frequently Asked Questions

What is the difference between displacement and distance?

Displacement is a vector that measures the straight-line change in position from start to end, including direction. Distance is a scalar that measures the total path length traveled regardless of direction. Displacement can be zero even when distance traveled is not (e.g., returning to start).

Which displacement formula should I use?

Use s = vt when you know average velocity and time. Use s = ½(v+u)t when you know initial and final velocities and time. Use s = ut + ½at² when you know initial velocity, acceleration, and time. The calculator lets you choose the formula based on the values you have available.

What units can I use with the displacement calculator?

The calculator supports meters, kilometers, feet, miles, centimeters, inches, and nautical miles for displacement. Time can be in seconds, minutes, or hours. Velocity units include m/s, km/h, ft/s, mi/h, and more.

Can displacement be negative?

Yes, displacement can be negative depending on the direction of motion. In one-dimensional motion, displacement is negative if the object moves in the opposite direction from the reference point. The calculator returns the magnitude; direction is indicated by the sign of the result.

What is the kinematic equation for displacement?

The most common kinematic equation for displacement is s = ut + ½at², where u is initial velocity, a is acceleration, and t is time. This equation assumes constant acceleration and is one of the fundamental equations of motion in classical mechanics.

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