Acceleration Calculator
Calculate acceleration from a change in velocity over time (a = Δv / Δt) or from force and mass (a = F / m). Mix units freely, pick your own positive direction, and get a plain-language reading of the result with a chart, a gauge, and step-by-step working.
Background
Acceleration is how quickly velocity changes, not how fast you are going. A car cruising at a steady 100 km/h has zero acceleration, while a car going from 0 to 20 m/s in 4 seconds has a lot. Because velocity has a direction, so does acceleration, and its sign only makes sense relative to the positive direction you choose.
How to use this calculator
- Choose Velocity and time if you know how the velocity changed and how long it took, or Force and mass if you know the net force on an object.
- Pick the positive direction that matches your diagram. Enter anything pointing the other way as a negative number.
- Enter just the numbers and choose units from the dropdowns. Units can be mixed, for example v₁ in km/h and v₂ in mph.
- Click Calculate (or press Enter). If something is missing or invalid, the calculator tells you which field and why.
How acceleration works
Acceleration measures how fast velocity changes, not how fast something is moving. Steady motion in a straight line, at any speed, means zero acceleration.
The sign of acceleration is about direction, not about speeding up or slowing down. An object speeds up when its velocity and acceleration point the same way, and slows down when they point opposite ways.
Δv / Δt gives the average acceleration over the interval. It equals the acceleration at every instant only if the acceleration is steady.
In F = m·a, F is the net force: every force along the axis added together, including friction and drag. The acceleration always points the same way as the net force.
One g is 9.80665 m/s², the acceleration due to gravity at Earth’s surface. Expressing an acceleration in g’s is a handy way to see how big it is.
Formula & Equations Used
Average acceleration: a = Δv ÷ Δt = (v₂ − v₁) ÷ Δt
Newton’s second law: F = m·a, so a = F ÷ m
Velocity to m/s: 1 km/h = 0.27778 m/s, 1 mph = 0.44704 m/s, 1 ft/s = 0.3048 m/s
Force and mass: 1 lbf = 4.44822 N, 1 lb = 0.45359237 kg
Acceleration units: a (ft/s²) = a (m/s²) ÷ 0.3048 and a (g) = a (m/s²) ÷ 9.80665
Example Problems & Step-by-Step Solutions
Example 1 — Speeding up
A car speeds up from 0 m/s to 20 m/s in 4 s.
Step: Δv = 20 − 0 = 20 m/s, then a = 20 ÷ 4.
Result: +5 m/s², about 0.51 g, in the positive direction.
Example 2 — Braking
A car slows from 72 km/h to a stop in 6 s.
Step: 72 km/h = 20 m/s, so Δv = 0 − 20 = −20 m/s and a = −20 ÷ 6.
Result: −3.33 m/s². The negative sign means the acceleration points opposite the car’s motion, which is why it slows down.
Example 3 — Force and mass
A net force of 300 N pushes a 50 kg cart.
Step: a = F ÷ m = 300 ÷ 50.
Result: +6 m/s² in the direction of the force.
Example 4 — Negative acceleration, but speeding up
With positive = →, a cart moving left goes from −5 m/s to −10 m/s in 2 s.
Step: Δv = −10 − (−5) = −5 m/s, so a = −5 ÷ 2.
Result: −2.5 m/s². The acceleration is negative, yet the cart is speeding up, because it is moving left and accelerating left.
Frequently Asked Questions
What units does acceleration use?
The SI unit is m/s². You will also see ft/s² and g, where 1 g ≈ 9.80665 m/s². This calculator shows all three.
Can acceleration be negative?
Yes. A negative value means the acceleration points opposite your chosen positive direction. That can mean slowing down, or speeding up in the negative direction.
Why is my acceleration negative if the object is speeding up?
Speeding up depends on velocity and acceleration pointing the same way. If the object is moving in the negative direction and accelerating in the negative direction, it speeds up while the acceleration is negative.
Does the positive-direction setting change the answer?
No. It changes the arrows and labels only. Enter values using your own convention, with a negative sign for anything pointing the other way, and the size of the acceleration stays the same.
What if my velocity units don’t match?
That’s fine. v₁ and v₂ can use different units, and both are converted to m/s internally.
Do I need net force or just one force?
For the force-and-mass method, enter the net force along the axis you chose: all forces added together, including friction and drag.
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