What is the difference between acceleration and velocity?

Velocity is the speed and direction of an object, while acceleration is the rate at which velocity changes. You can have high velocity with zero acceleration (constant speed) or zero velocity with high acceleration (the instant you throw a ball upward at its peak).

Can acceleration be negative?

Yes. Negative acceleration (deceleration or retardation) means the object is slowing down relative to its direction of motion. When you apply brakes in a car moving forward, the acceleration is negative.

What is gravitational acceleration?

Gravitational acceleration (g) is approximately 9.81 m/s^2 on Earth's surface. It is the rate at which objects accelerate when falling freely, regardless of their mass (ignoring air resistance).

How does mass affect acceleration?

According to Newton's second law (F = ma), for a given force, a larger mass results in smaller acceleration. Doubling the mass halves the acceleration if the applied force remains the same.

What units are used for acceleration?

The SI unit is meters per second squared (m/s^2). In everyday contexts, acceleration is sometimes expressed in g-forces, where 1g = 9.81 m/s^2. Fighter pilots experience up to 9g during maneuvers.

Acceleration Calculator

Calculate acceleration from change in velocity and time (a = Δv / Δt)

Acceleration Calculator

Calculate acceleration (a = dv / dt)

Acceleration

a = (v - u) / t

Initial Velocity (m/s)

Final Velocity (m/s)

Time (s)

Formula

a = (v - u) / t

What Is Acceleration?

Acceleration is the rate of change of velocity over time. An object accelerates when it speeds up, slows down, or changes direction. It is a vector quantity — it has both magnitude and direction. The SI unit is meters per second squared (m/s²). Earth's gravitational acceleration is approximately 9.81 m/s², meaning a freely falling object gains about 9.81 m/s of speed every second it falls.

This calculator solves for any of the three variables in the acceleration equation: acceleration (a), change in velocity (Δv), or time interval (Δt). Enter any two known values to find the third. Results are also converted between m/s², ft/s², and g-force so you can work in whichever unit fits your problem.

How to Use the Acceleration Calculator

Select what you want to calculate — acceleration, velocity change, or time interval.
Enter the two known values along with their units.
Click Calculate to run the computation.
Read the result and review the automatic unit conversions below it.

Formulas & Unit Conversions

a = Δv / Δt  =  (v_final − v_initial) / t

Solving for velocity change:
  Δv = a × t

Solving for time:
  t = Δv / a

Unit conversions:
  1 g = 9.81 m/s² ≈ 32.17 ft/s²

Kinematic equations:
  v = v₀ + at
  s = v₀t + ½at²
  v² = v₀² + 2as

Average acceleration assumes constant acceleration throughout the interval. For varying acceleration, instantaneous acceleration is found by taking the derivative of the velocity function with respect to time (a = dv/dt).

Real-World Examples

Car accelerating from 0 to 60 mph in 5 seconds

60 mph = 26.8 m/s. a = 26.8 m/s ÷ 5 s = 5.36 m/s² ≈ 0.55 g. A typical sports car produces around 0.5–0.8 g of forward acceleration.

Emergency braking from 30 m/s to a stop in 6 seconds

Δv = 0 − 30 = −30 m/s. a = −30 ÷ 6 = −5 m/s². The negative sign indicates deceleration (the vehicle is slowing down). Anti-lock brakes can achieve roughly −8 to −10 m/s².

Free fall near Earth's surface (ignoring air resistance)

Any object in free fall accelerates downward at g ≈ 9.81 m/s². After 3 seconds of free fall, its speed reaches 3 × 9.81 = 29.43 m/s (≈ 66 mph). Air resistance reduces this for real-world objects.

Frequently Asked Questions

What is the difference between speed and velocity?▾

Speed is a scalar — it tells you how fast something is moving but not in which direction. Velocity is a vector — it includes both magnitude and direction. Because acceleration depends on the change in velocity, an object moving in a circle at constant speed still accelerates because its direction is constantly changing.

What does negative acceleration mean?▾

Negative acceleration (also called deceleration) means the object is slowing down in the positive direction, or speeding up in the negative direction. The sign depends on your chosen coordinate system. For example, if you define 'forward' as positive, braking produces a negative acceleration value.

What is g-force?▾

G-force (or g) is acceleration expressed as a multiple of Earth's standard gravitational acceleration, g ≈ 9.81 m/s². At 1 g you feel your normal weight; at 2 g everything feels twice as heavy. Fighter pilots can withstand up to about 9 g with specialized suits. Roller coasters typically peak around 3–5 g.

How does acceleration relate to force?▾

Newton's Second Law states F = ma — force equals mass times acceleration. If you know the net force acting on an object and its mass, you can find its acceleration with a = F / m. Conversely, if you measure the acceleration and know the mass, you can work out the net force.

What is terminal velocity?▾

Terminal velocity is the constant speed a falling object reaches when the drag force from air resistance equals the gravitational force pulling it down. At that point, net force is zero and acceleration drops to zero. For a skydiver in a belly-to-earth position, terminal velocity is roughly 55 m/s (about 195 km/h or 120 mph).