What this calculator does
Change in velocity, often written Δv or called delta-v, is simply the final velocity minus the initial velocity: how much an object sped up, slowed down, or changed direction over some interval. This calculator finds it either directly, from a starting and ending speed, or by working forward from a known acceleration and the time it acted over.
People asking how to calculate change in velocity are usually one step short of a full acceleration problem: they already know two of the values acceleration, time, initial speed or final speed, and just want the speed difference itself, not the rate at which it happened. Keeping Δv separate from acceleration avoids conflating "how much did the speed change" with "how quickly did it change".
The formula
With an initial and final velocity, Δv is just final minus initial: a positive result means speeding up, a negative result means slowing down. Given acceleration and time instead, Δv equals acceleration multiplied by time, which is the same quantity worked out the other way around, since a = Δv/t rearranges directly to Δv = a·t.
| Term | Meaning |
|---|---|
| Δv (delta-v) | Change in velocity: final velocity minus initial velocity, or acceleration times time. |
| Initial velocity (u) | The speed at the start of the interval being measured. |
| Final velocity (v) | The speed at the end of the interval being measured. |
| Acceleration (a) | The rate of change of velocity, used with time when the two speeds are not both known directly. |
The inputs explained
| Field | What to enter |
|---|---|
| Calculate from | Choose whether to enter the two speeds directly, or an acceleration and a time instead. |
| Initial velocity (km/h) | The starting speed, used when calculating from the two velocities. |
| Final velocity (km/h) | The ending speed, used when calculating from the two velocities. |
| Acceleration (m/s²) | The acceleration, used when calculating from acceleration and time. |
| Time (s) | The time over which that acceleration acted, used when calculating from acceleration and time. |
When to use it
Working from a before-and-after speed reading
A speed measured at two points, such as before and after braking, gives Δv directly without needing to know anything about how the speed changed in between.
Working from a known acceleration
When acceleration and duration are known instead, such as from a rated 0-to-highway-speed time, this finds the resulting speed change without needing separate before-and-after readings.
Checking a step inside a larger physics problem
Δv is an intermediate quantity in many kinematics and momentum problems; isolating it on its own keeps that one step easy to check before it feeds into a bigger calculation.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Delta-v from 0 up to a range of final speeds
Initial velocity held at 0 km/h, with final velocity varied, using the direct two-velocity mode.
| Final velocity | Change in velocity (Δv) | Same, in km/h |
|---|---|---|
| 20 km/h | 5.556 m/s | 20.00 km/h |
| 40 km/h | 11.111 m/s | 40.00 km/h |
| 60 km/h | 16.667 m/s | 60.00 km/h |
| 80 km/h | 22.222 m/s | 80.00 km/h |
| 100 km/h | 27.778 m/s | 100.00 km/h |
| 120 km/h | 33.333 m/s | 120.00 km/h |
Delta-v from a fixed acceleration over a range of times
A constant acceleration of 3 m/s², with the time it acts over varied, using the acceleration-and-time mode.
| Time | Change in velocity (Δv) | Same, in km/h |
|---|---|---|
| 2 s | 6.000 m/s | 21.60 km/h |
| 4 s | 12.000 m/s | 43.20 km/h |
| 6 s | 18.000 m/s | 64.80 km/h |
| 8 s | 24.000 m/s | 86.40 km/h |
| 10 s | 30.000 m/s | 108.00 km/h |
| 12 s | 36.000 m/s | 129.60 km/h |
Questions
How do you find change in velocity?
Subtract the initial velocity from the final velocity (Δv = v − u) if both speeds are known. If instead you know the acceleration and how long it acted, multiply the two together (Δv = a × t), which gives the same result by rearranging the definition of acceleration.
What does a negative change in velocity mean?
A negative Δv means the object slowed down or reversed direction along the axis being measured, since the final velocity is lower than the initial one. The magnitude is the same size of change either way; only the sign flips.
Is change in velocity the same as acceleration?
No. Change in velocity is the total difference in speed over the whole interval, in units of speed. Acceleration is the rate at which that change happens, in units of speed per unit of time. The two are related by Δv = a × t, but they answer different questions.
Does change in velocity depend on direction?
Yes, when velocity is treated as a vector, a change in direction alone (even at constant speed) counts as a change in velocity. This calculator handles the straight-line case, where only speeding up or slowing down along one direction is considered.
For the acceleration rate itself, along with stopping distance, see the acceleration calculator. For the related change in momentum from a mass and a speed change, see the momentum calculator.