Example 1
A compact car gains 27.8 m/s from rest in 8 s, about 100 km/h or about 62 mph. The panel shows 3.48 m/s².
a = 3.48 m/s²
Acceleration Calculator
Enter the speed change in meters per second and the time in seconds. The calculator finds average acceleration from a = Δv/t, which is a = (v − v₀)/t. For 27.8 m/s and 8 s the result is 3.48 m/s². The model does not compute distance or the force F = m·a.
Result
Enter a speed change and a time. Acceleration, the g reading, and the chart will appear here.
Distance and final speed at a known a are on the uniformly accelerated motion calculator. Stopping distance is on the uniformly decelerated motion calculator. Force is on the F = ma calculator.
How it works
Δv27.8 m/s
t8 s
a3.48 m/s²
Average acceleration says how much speed changes per second over a chosen interval. The formula a = Δv/t is the same statement as a = (v − v₀)/t when Δv is the difference between the final speed and the initial speed and t is the duration of that change. For 27.8 m/s and 8 s the quotient is 3.475 m/s², and the panel rounds it to 3.48 m/s².
The calculator uses the numbers you enter: a speed change Δv in meters per second and a time t in seconds. Enter 100 km/h as 27.8, not as 100. The quotient of 13.9 m/s and 8 s, about 50 km/h, is 1.74 m/s² on the panel. The same change of 27.8 m/s in 10 s gives 2.78 m/s². A comma and a period are the same decimal separator.
What the result panel shows. Besides acceleration, the calculator reports the entered Δv in m/s and in km/h, the time, the quotient a/9.81, and the acceleration over twice the time. For 27.8 m/s and 8 s the g reading is 0.35 g, and the same change in 16 s gives 1.74 m/s². The chart draws a = Δv/t at 2, 4, 6, 8, and 12 s for that same speed change.
Limits of the model. The result is the average over the whole interval, not the derivative dv/dt. The calculator does not compute the distance s = v₀t + ½at², does not multiply by mass in F = ma, and does not convert kilometers per hour into meters per second. Distance at constant a is on the uniformly accelerated motion page, force is on the F = ma page, and stopping distance is on the uniformly decelerated motion page. A negative speed change gives a negative a.
The unit switch in the header converts meters per second to feet per second and m/s² to ft/s² by the factor 3.2808399, and it converts a number already entered in the speed field. Time stays in seconds. The values in this text stay in SI units as the reference.
The examples on this page use the same quotient. 27.8 m/s in 8 s gives 3.48 m/s². 10 m/s in 2 s gives 5.00 m/s². A change of −25 m/s in 3 s gives -8.33 m/s². The button “Fill this example” enters those numbers and refreshes the panel and the chart.
Formula
a = Δv / t = (v − v0) / t
[a] = (m/s) / s = m/s²
Model: average acceleration from the textbook definition. On the third day of the Discorsi (1638), Galileo described motion that gains equal speed increments in equal times. The symbol a and the line a = Δv/Δt came later. This calculator takes a speed change Δv that you have already found, plus a time t. It has no separate fields for v and v₀. Order of operations: a = Δv/t in SI units, then a/9.81, then a over the time 2t.
Theory, definition, and scope
Definition of average acceleration
Average acceleration over a time t is a = (v − v₀)/t. The difference v − v₀ is Δv. The SI unit is the meter per second squared. For 27.8 m/s and 8 s the steps are short. Step 1: Δv = 27.8 m/s. Step 2: 27.8 / 8 = 3.475 m/s². Step 3: the panel rounds to two decimal places and shows 3.48 m/s². The same change in 10 s gives 2.78 m/s², and in 16 s it gives 1.74 m/s², because a longer time lowers the quotient.
Galileo and equal speed increments
In Discorsi e dimostrazioni matematiche intorno a due nuove scienze (Leiden, 1638), on the third day, Galileo defined naturally accelerated motion as motion in which equal speed increments arise in equal times. He timed an incline with a water clock, so the fall was slow enough to measure. He did not write a = Δv/t in modern notation. The definition of average acceleration is the textbook reading of that property. Mechanics textbooks state it the same way, including Halliday, Resnick, and Walker, and OpenStax College Physics, section 2.4.
Instantaneous acceleration
Instantaneous acceleration is the limit of Δv/Δt as Δt approaches zero, the derivative dv/dt. When acceleration is constant, the average and the instantaneous value match. When the force or the slope changes with time, the average over the whole interval does not describe one instant. The calculator does not take that limit and does not read a v(t) graph. It returns one quotient from two numbers you enter.
The SI unit and the g reading
The meter, the second, and the derived units are defined in the SI Brochure (BIPM, 9th edition). The g reading on the panel divides a by 9.81 m/s². The Third General Conference on Weights and Measures in 1901 adopted the standard acceleration gn = 9.80665 m/s², and NIST lists the same value. The calculator does not substitute 9.80665. For 27.8 m/s and 8 s, the unrounded quotient divided by 9.81 is about 0.354, and the panel shows 0.35 g.
Distance, force, and Newton’s second law
At constant acceleration, distance from an initial speed v₀ is s = v₀t + ½at², and the final speed is v = v₀ + at. This form does not compute those quantities, because it has no v₀ field and no distance field. The school form of Newton’s second law, F = ma, links force to acceleration. Newton stated the relation of force to change of motion in the Principia (1687). There is no mass here, so the calculator does not report newtons. As an illustration only: a mass of 1,000 kg at 3.48 m/s² would need a force of about 3,480 N, but that product belongs on the F = ma page, not in this quotient.
The figure 3,480 N is only an illustration of F = ma at the rounded 3.48 m/s² and a mass of 1,000 kg. 3.48 × 1,000 = 3,480. The unrounded 3.475 × 1,000 = 3,475 N. This page’s panel shows neither force.
Outside the formula
The formula does not cover centripetal acceleration v²/r, gravitational acceleration GM/r², or air resistance. It also does not cover the reaction distance before braking. A negative Δv is allowed and gives a negative a. For −25 m/s and 3 s the panel shows -8.33 m/s². The distance over which that change happens stays on the decelerated-motion page. Instantaneous acceleration from a phone sensor is a different measurement: that is a vector and a short time step, while this page is one interval.
Sources
The definition and the unit come from mechanics textbooks and from metrology: D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics, kinematics chapters; OpenStax, College Physics 2e, section 2.4; G. Galilei, Discorsi, 1638, third day; I. Newton, Philosophiæ Naturalis Principia Mathematica, 1687; BIPM, SI Brochure, 9th edition; NIST, standard acceleration of gravity. This page is educational.
How to use it
- Enter the speed change in meters per second, for example 27.8. 100 km/h is 27.8, not 100. A minus sign means the speed fell.
- Enter the time in seconds, for example 8. A minute is 60 seconds. A time of zero is rejected.
- Click Calculate, or wait for the live result. For 27.8 m/s and 8 s the calculator shows 3.48 m/s².
- Check the panel: speed in km/h, the reading a/9.81, and the acceleration over twice the time. The chart uses the same speed change at 2, 4, 6, 8, and 12 s.
- Clearing the form removes the numbers you entered and hides the panel. The examples enter ready pairs of speed change and time, including a speed drop with a minus sign.
Symbol glossary
a is average acceleration, Δv is the speed change, and t is time. For 27.8 m/s and 8 s the result is 3.48 m/s².
- a
- Average acceleration [m/s²], a = Δv/t. The panel rounds to two decimal places.
- Δv
- Speed change [m/s], the first field. Enter 100 km/h as 27.8. A minus sign means the speed decreased.
- t
- Time [s]. It must be greater than zero. A minute is 60 s.
- v₀
- Initial speed. This form does not have that field. You enter the difference v − v₀.
- g
- The reading a/9.81. Conventional gn is 9.80665 m/s². The script uses 9.81.
- 2t
- Twice the time. The same Δv then gives half the acceleration.
Worked examples
Example 2
A gentle start takes 12 s and changes the speed by 11.1 m/s, about 40 km/h or about 25 mph. The panel shows 0.92 m/s².
a = 0.92 m/s²
Example 3
A run from rest to 25 m/s takes 3 s and ends at 90 km/h, about 56 mph. The panel shows 8.33 m/s². This is a speed increase, not braking.
a = 8.33 m/s²
Example 4
In the first 2 s of a run, the speed change is 10 m/s. The panel shows 5.00 m/s².
a = 5.00 m/s²
Example 5
A short acceleration raises the speed to 2.5 m/s in 2 s. The panel shows 1.25 m/s².
a = 1.25 m/s²
Example 6
An airliner takeoff roll reaches 69.4 m/s in 35 s, about 250 km/h or about 155 mph. The panel shows 1.98 m/s².
a = 1.98 m/s²
Example 7
A bicycle gains 5.6 m/s in 5 s, about 20 km/h or about 12.5 mph. The panel shows 1.12 m/s².
a = 1.12 m/s²
Example 8
A long speed buildup takes 80 s and changes the speed by 44.4 m/s, about 160 km/h or about 99 mph. The panel shows 0.55 m/s².
a = 0.55 m/s²
Example 9
The same change of 27.8 m/s takes 2.3 s. The panel shows 12.09 m/s².
a = 12.09 m/s²
Example 10
A metro train gains 16.7 m/s in 15 s, about 60 km/h or about 37 mph. The panel shows 1.11 m/s².
a = 1.11 m/s²
Example 11
In free fall, speed increases by 9.81 m/s in each second on the scale the panel uses. The result is 9.81 m/s².
a = 9.81 m/s²
Example 12
Speed falls by 25 m/s in 3 s, for example from 25 m/s to zero. The field receives −25. The panel shows -8.33 m/s². Distance is on another page.
a = -8.33 m/s²
Common questions
What does this calculator compute, and which formula does it use?
The calculator finds average acceleration from a = Δv/t, which is a = (v − v₀)/t when the first field is already the speed difference. For 27.8 m/s and 8 s the panel shows 3.48 m/s².
Which units should I enter for the speed change and the time?
Enter the speed change in meters per second and the time in seconds. The result is in m/s². 100 km/h is 27.8 m/s, not the number 100. After you switch the header to US units, speed is in ft/s and acceleration is in ft/s². Time stays in seconds. A comma and a period are the same decimal separator.
Why not enter a speedometer reading directly?
The field expects meters per second. 100 km/h corresponds to 27.8 m/s, and about 50 km/h corresponds to 13.9 m/s. The number 100 in the field means 100 m/s. The header switch does not convert kilometers per hour into meters per second. Do that conversion before you enter the number. A minute is 60 seconds, not 1.
What happens when the time is zero or negative?
The calculator rejects a time of zero and a negative time, because it divides by t. Both fields need a number. When both fields are empty, the panel stays hidden and no error message appears.
Is the result average acceleration or instantaneous acceleration?
The result is the average acceleration over the time you enter. Instantaneous acceleration is the limit of Δv/Δt as the time interval shrinks toward zero, the derivative dv/dt. The calculator does not take that limit. The chart is not a plot of instantaneous acceleration either. It shows how the average falls when the same speed change takes longer.
Can the speed change be negative or zero?
Yes. A negative Δv gives a negative a and means the speed decreased. Zero in the speed-change field, with a positive time, gives 0 m/s². For a change of −25 m/s in 3 s the panel shows -8.33 m/s². Stopping distance is on the decelerated-motion page, because this formula does not compute a distance.
What do the panel and the chart show?
The panel reports acceleration, the speed change in m/s and in km/h, the time, the quotient a/9.81, and the acceleration over twice the time. For 27.8 m/s and 8 s those are 3.48 m/s², 0.35 g, and 1.74 m/s² at 16 s. The bar chart evaluates Δv/t at 2, 4, 6, 8, and 12 s. “Fill this example” enters the example numbers and refreshes the panel and the chart. The fields start empty.
How is this different from distance under constant acceleration?
Here the inputs are a speed change and a time, and the result is a. On the uniformly accelerated motion page the inputs are a constant a, an initial speed, and a time, and the results are distance and final speed. The formula s = v₀t + ½at² assumes a constant a. This calculator does not check whether acceleration stayed constant inside the interval. It reports only the average.
Where does the g reading come from, and why is the divisor 9.81?
The panel divides the result by 9.81 m/s². That is the rounded standard gravity used in the script. The standard acceleration of gravity adopted by the Third General Conference on Weights and Measures in 1901 is exactly 9.80665 m/s². The calculator does not substitute that more precise constant. For the quotient 27.8 / 8 the reading is 0.35 g.
Does the result include friction, air resistance, or a changing force?
No. The formula divides the speed change you enter by the time you enter. It does not subtract friction, it does not model drag, and it does not require the force to be constant. If the speed rose unevenly, the result is still the average over that interval. Force F = ma has its own page, because there is no mass field here.
How do I calculate acceleration with a = Δv/t?
Divide the speed change in m/s by the time in seconds. For 27.8 m/s and 8 s: 27.8/8 = 3.475 ≈ 3.48 m/s² on the panel.
How do I convert 100 km/h into Δv in m/s?
Divide by 3.6. 100 km/h is about 27.8 m/s. Enter 27.8 in the field, not 100.
What is a when braking from 20 m/s to rest in 4 s?
Δv = −20 m/s, so a = −20/4 = −5 m/s². The minus sign means speed decreases in the chosen positive direction.
How is this result different from a = F/m?
Here the quotient comes from a speed change and a time. Force and mass are not fields on this page; a = F/m belongs to a separate dynamics calculator.
How does this acceleration differ from centripetal acceleration?
Here Δv is a linear speed change over time. Centripetal acceleration v²/r is for circular motion and has its own page.
Sources
The definition, the unit, and the history of equal speed increments come from physics and metrology sources. This page does not invent publication identifiers.
- Wikipedia — Acceleration
- OpenStax — College Physics 2e, section 2.4, Acceleration
- BIPM — The International System of Units (SI), 9th edition
- NIST — standard acceleration of gravity, gn = 9.80665 m/s²
- Galilei, G., Discorsi e dimostrazioni matematiche intorno a due nuove scienze, Leiden, 1638, third day.
- Newton, I., Philosophiæ Naturalis Principia Mathematica, 1687.
Page updated November 3, 2026.