On this page
Formula
a = (v − v₀) ÷ t, a = 2(d − v₀t) ÷ t², a = F ÷ m
- a
- acceleration, in meters per second squared (m/s²)
- v₀, v
- initial and final velocity, in meters per second (m/s)
- t
- elapsed time, in seconds (s)
- d
- distance traveled during that time, in meters (m)
- F, m
- net force in newtons (N) and mass in kilograms (kg)
What acceleration means
Acceleration is the rate at which velocity changes. An acceleration of 3 m/s² means the velocity grows by 3 m/s every second: 0, 3, 6, 9 m/s and so on. Because velocity has a direction, slowing down and turning are accelerations too. In everyday language, slowing down is called deceleration. In the calculator it appears as a negative acceleration.
The SI unit is the meter per second squared (m/s²). Drivers often think in “0 to 60 mph” times, and pilots and engineers in multiples of g, so the acceleration calculator shows all of these.
Three ways to calculate acceleration
| You know | Mode | Formula |
|---|---|---|
| Starting speed, final speed and time | Velocity change | a = (v − v₀) ÷ t |
| Distance, time and starting speed | Distance & time | a = 2(d − v₀t) ÷ t² |
| Net force and mass | Force & mass | a = F ÷ m |
The first is the definition of average acceleration. The second comes from the constant-acceleration equation d = v₀t + ½at², solved for a. The third is Newton’s second law, the same one the force calculator uses.
How to use the acceleration calculator
- Choose the mode that matches what you know.
- Enter the values and pick a unit for each. Speeds can be in m/s, km/h, mph, ft/s or knots. Times can be in seconds, minutes or hours. Distance can be in meters, kilometers, feet or miles.
- Choose how to show the answer: m/s², ft/s², g, km/h per second or mph per second.
- Below the answer you get the g-force equivalent and the speed gained each second. Depending on the mode, you also see the distance covered or the final velocity.
How to calculate acceleration by hand
From a change in velocity. A train goes from 0 to 27 m/s in 9 s. a = (27 − 0) ÷ 9 = 3 m/s², which is 3 ÷ 9.80665 ≈ 0.31 g.
From distance and time. A cart starts from rest and rolls 80 m in 4 s with constant acceleration. a = 2 × (80 − 0 × 4) ÷ 4² = 160 ÷ 16 = 10 m/s².
From force and mass. A net force of 900 N acts on a 60 kg sled. a = 900 ÷ 60 = 15 m/s².
When speeds are in mph or km/h, convert them to m/s first. Divide km/h by 3.6, or multiply mph by 0.44704. Otherwise the answer comes out in odd units such as km/h per second, which is a valid unit but easy to misread.
Car acceleration: 0–60 mph times in m/s² and g
The average acceleration for common 0–60 mph times, assuming constant acceleration:
| 0–60 mph time | m/s² | ft/s² | g |
|---|---|---|---|
| 3 s | 8.941 | 29.33 | 0.912 |
| 4 s | 6.706 | 22 | 0.684 |
| 5 s | 5.364 | 17.6 | 0.547 |
| 6 s | 4.47 | 14.67 | 0.456 |
| 8 s | 3.353 | 11 | 0.342 |
| 10 s | 2.682 | 8.8 | 0.274 |
| 12 s | 2.235 | 7.333 | 0.228 |
Real cars accelerate harder at low speed and less near 60 mph, so these are averages over the run.
Real-life uses
Cars and braking
Acceleration and braking figures are easier to compare in g. Braking from 60 mph to a stop in 3 seconds averages about 0.91 g, while a gentle stop over 10 seconds is only 0.27 g.
Roller coasters and aircraft
Ride designers and pilots work in g because it describes how heavy riders feel. Sustained forces of several g need special training or equipment.
Sports
Sprinters reach their highest acceleration in the first few steps out of the blocks. Splitting a race into intervals and applying a = Δv ÷ t to each one shows where the speed is gained.
Homework and labs
In a cart-and-ramp experiment you measure distance and time, which is exactly the distance & time mode. To go on and find the final speed, use the velocity calculator. To convert speeds between units, use the speed converter.
Common mistakes
- Using distance ÷ time². a = d ÷ t² is off by a factor of 2. From rest, a = 2d ÷ t².
- Ignoring the initial velocity. If the object was already moving, subtract v₀t from the distance first.
- Mixing units. km/h with seconds gives km/h per second. Convert to m/s first.
- Dropping the sign. A braking car has negative acceleration. The magnitude is the deceleration.
- Using total force instead of net force in a = F ÷ m.
Glossary
- Velocity: speed in a given direction.
- Average acceleration: total change in velocity divided by total time.
- Deceleration: acceleration opposite to the direction of motion.
- g-force: acceleration expressed as a multiple of standard gravity, 9.80665 m/s².
- Uniform acceleration: acceleration that stays constant, which the kinematic equations assume.
Worked examples
A car going 0 to 60 mph
A car reaches 60 mph from a standstill in 7.5 seconds.
Inputs (Velocity change): Initial velocity (v₀) = 0; Initial velocity (v₀) unit = Miles per hour; Final velocity (v) = 60; Final velocity (v) unit = Miles per hour; Time = 7.5; Time unit = Seconds; Show acceleration in = Meters per second squared (m/s²)
Convert to SI units: 0 mph = 0 m/s; 60 mph = 26.8224 m/s a = (v − v₀) ÷ t = (26.8224 m/s − 0 m/s) ÷ 7.5 s = 3.57632 m/s²
Answer: From 0 mph to 60 mph in 7.5 s: acceleration 3.57632 m/s² (0.3647 g).
Braking to a stop
A vehicle slows from 25 m/s to rest in 4 seconds. The negative sign means deceleration.
Inputs (Velocity change): Initial velocity (v₀) = 25; Initial velocity (v₀) unit = Meters per second; Final velocity (v) = 0; Final velocity (v) unit = Meters per second; Time = 4; Time unit = Seconds; Show acceleration in = Meters per second squared (m/s²)
a = (v − v₀) ÷ t = (0 m/s − 25 m/s) ÷ 4 s = −6.25 m/s²
Answer: From 25 m/s to 0 m/s in 4 s: acceleration −6.25 m/s² (−0.6373 g).
From distance and time, starting at rest
An object starts from rest and covers 50 m in 5 s at constant acceleration.
Inputs (Distance & time): Distance = 50; Distance unit = Meters; Time = 5; Time unit = Seconds; Initial velocity (v₀) = 0; Initial velocity (v₀) unit = Meters per second; Show acceleration in = Meters per second squared (m/s²)
a = 2 × (d − v₀ × t) ÷ t² = 2 × (50 m − 0 m/s × 5 s) ÷ (5 s)² = 4 m/s²
Answer: Covering 50 m in 5 s from 0 m/s: acceleration 4 m/s² (0.4079 g).
Edge case: US units, answer in g
A net force of 450 lbf on a 150 lb mass. One pound-force is the weight of one pound, so the acceleration is 450 ÷ 150 = 3 g exactly.
Inputs (Force & mass): Net force = 450; Net force unit = Pounds-force; Mass = 150; Mass unit = Pounds; Show acceleration in = Standard gravity (g) (g)
Convert to SI units: 450 lbf = 2,001.7 N; 150 lb = 68.0389 kg a = F ÷ m = 2,001.7 N ÷ 68.0389 kg = 29.42 m/s² 29.42 m/s² = 3 g
Answer: A net force of 450 lbf on 150 lb: acceleration 3 g.
Assumptions and limitations
- Acceleration is assumed constant over the interval. If it varies, the result is the average acceleration over that time.
- Motion is along a straight line. A negative result means the object is slowing down (decelerating) in its direction of travel.
- The distance mode uses the constant-acceleration equation d = v₀t + ½at². If the numbers would require the object to reverse direction, the result shows a warning.
- The force mode uses the net force (F = ma). Subtract friction and drag before entering it.
- The g-force equivalent uses standard gravity, 9.80665 m/s². Results are shown to 6 significant figures, and g values to 4.
Frequently asked questions
What is the formula for acceleration?
Average acceleration is the change in velocity divided by the time taken, a = (v − v₀) ÷ t. If a car goes from 0 to 27 m/s in 9 s, its acceleration is 27 ÷ 9 = 3 m/s².
How do I calculate acceleration from distance and time?
If the acceleration is constant, use a = 2(d − v₀t) ÷ t². Starting from rest, this becomes a = 2d ÷ t². An object that covers 80 m in 4 s from rest accelerates at 2 × 80 ÷ 16 = 10 m/s².
How do I calculate acceleration from force and mass?
Divide the net force by the mass, a = F ÷ m. A net force of 900 N on a 60 kg mass gives 15 m/s².
What does a negative acceleration mean?
That the velocity is decreasing in the direction you chose as positive, usually called deceleration. A car braking from 20 m/s to 0 in 5 s has an acceleration of −4 m/s².
How do I convert 0–60 mph time to acceleration?
60 mph is 26.8224 m/s, so divide that by the time in seconds. A 6-second 0–60 time is 26.8224 ÷ 6 ≈ 4.47 m/s², or about 0.46 g.
What is 1 g of acceleration?
Standard gravity, 9.80665 m/s² (about 32.17 ft/s²). Expressing acceleration in g shows how it compares with the pull of Earth's gravity. 0.5 g feels like half your weight pushing you into the seat.
What are the units of acceleration?
Meters per second squared (m/s²) in SI, which means the velocity changes by so many m/s every second. Feet per second squared, g, and mph per second are also common.
Sources
- University Physics Volume 1, 3.3 Average and Instantaneous Acceleration — OpenStax (Rice University). Checked October 12, 2026.
- University Physics Volume 1, 3.4 Motion with Constant Acceleration — OpenStax (Rice University). Checked October 12, 2026.
- CODATA value: standard acceleration of gravity — NIST Physical Measurement Laboratory. Checked October 12, 2026.