What is the formula for displacement?

The most common SUVAT formula is s = ut + 0.5at², where s is displacement, u is initial velocity, a is acceleration, and t is time. When you know initial and final velocities and acceleration instead, use s = (v² - u²) divided by 2a. Both give the same result when the motion is under constant acceleration.

What is the difference between displacement and distance?

Distance is the total length of path travelled, regardless of direction. Displacement is the straight-line change in position from start to finish, including direction. If you walk 5 m east and then 5 m west, the distance is 10 m but the displacement is zero.

How far does an object fall in 3 seconds?

Using s = ut + 0.5at² with initial velocity u = 0 and acceleration a = 9.81 m/s² (gravity): s = 0 + 0.5 times 9.81 times 9, which equals 44.15 metres. This is the distance fallen from rest under gravity alone, ignoring air resistance.

Displacement Calculator

Displacement is the straight-line change in position of an object from its starting point to its ending point, including direction. It is one of the five SUVAT quantities that describe motion under constant acceleration, and this calculator solves for it using whichever combination of values you have. In the first mode you enter the initial velocity, the constant acceleration, and the elapsed time, and the calculator applies the equation s = ut + 0.5at2 to find how far the object has moved. This is the most common form: an object starting at rest and falling under gravity, for example, has zero initial velocity and an acceleration of 9.81 m/s2 downward. In the second mode you enter the initial velocity, the final velocity, and the acceleration, and the calculator uses s = (v2 - u2) / 2a. This is handy when you know how fast something started and ended but not how long it took. Both equations assume constant acceleration throughout the motion. The calculator also returns the final velocity (from the first mode) and the average velocity over the interval, so you get a full picture of the motion with a single calculation. Results update as you type. A note on signs: enter negative values for deceleration or motion in the opposite direction. The default example has an object starting from rest (u = 0), accelerating at 9.81 m/s2 for 3 s, which gives a displacement of 44.15 m, equivalent to free fall under gravity for three seconds. Use this tool for physics homework, projectile and freefall problems, or any situation involving constant acceleration.

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Formula

Initial velocity (u)

m/s

Acceleration (a)

m/s²

Time (t)

44.15 m

displacement

Final velocity29.43 m/s

Average velocity14.72 m/s

Time elapsed3.00 s

Assumes constant acceleration. Use negative values for deceleration or reversed direction. Results in SI units, rounded for display.

How it works

In the first mode the calculator uses s = ut + 0.5at², where u is initial velocity, a is acceleration, and t is time. It also computes the final velocity as v = u + at and the average velocity as (u + v) / 2. In the second mode it uses s = (v² - u²) / 2a, rearranged from the SUVAT identity v² = u² + 2as. Both equations assume constant acceleration throughout the interval.

Worked example

An object starts from rest (u = 0 m/s) and accelerates at 9.81 m/s2 for 3 s (free fall under gravity). Displacement = 0 times 3 + 0.5 times 9.81 times 9 = 44.15 m. The final velocity is 0 + 9.81 times 3 = 29.43 m/s and the average velocity is 14.72 m/s. These match the default values pre-filled above.

Related calculators

SUVAT Calculator: solve any SUVAT variable given three others.
Average Velocity Calculator: find average velocity from total displacement and time.
Velocity Calculator: find instantaneous velocity.
Kinetic Energy Calculator: convert velocity to energy.

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