Acceleration Calculator
Calculate average acceleration from initial velocity, final velocity, and elapsed time, with a signed result in m/s².
How It's Calculated
Formula
a = \dfrac{v_2 - v_1}{t}Average acceleration is the change in velocity (final velocity minus initial velocity) divided by the elapsed time, in meters per second squared. Velocity is signed: entering a smaller final velocity than initial velocity (or a negative value) produces a negative acceleration result. A negative result means velocity decreased relative to whichever direction was treated as positive when the values were entered — it is not automatically labeled "deceleration", since that label depends on the chosen coordinate direction, not on the arithmetic. This is distinct from the Speed Calculator, which computes a non-negative scalar speed from distance and time, and from the Force Calculator's acceleration input, which is a non-negative magnitude only.
Worked Examples
0 to 20 m/s in 4 seconds
- Acceleration = (20 m/s - 0 m/s) / 4 s = 5 m/s².
20 to 0 m/s in 4 seconds
- Acceleration = (0 m/s - 20 m/s) / 4 s = -5 m/s². Velocity decreased, so the result is negative.
-10 to 10 m/s in 5 seconds
- Acceleration = (10 m/s - (-10 m/s)) / 5 s = 20 m/s / 5 s = 4 m/s².
Frequently Asked Questions
Is this the same as the Speed Calculator?
No. This calculator computes average acceleration from a change in velocity over elapsed time (a = (v2 - v1) / t), and velocity may be signed. The Speed Calculator instead computes a non-negative scalar speed from distance and time and has no velocity or sign concept.
Does a negative result mean deceleration?
Not necessarily. A negative acceleration result simply means velocity decreased relative to whichever direction was entered as positive. Whether that is called "deceleration" depends on the chosen coordinate direction, so this calculator reports the signed value without renaming it.
Can initial or final velocity be negative?
Yes. Both are signed finite numbers and may be negative, zero, or positive.
Why must time be positive?
Acceleration is a change in velocity divided by time, which is undefined for zero or negative time (division by zero or a meaningless negative duration), so time must be a positive number.