Acceleration Calculator
Acceleration is the rate at which velocity changes, and it shows up everywhere a speed changes: a car pulling away from a light, a train braking for a station, a sprinter leaving the blocks. The same one-line definition, change in velocity divided by time, answers all of them, but real problems do not always hand you the time. Sometimes you know the distance instead, and sometimes the question starts from force and mass rather than motion at all.
The Acceleration Calculator below covers all four routes in one card. Find acceleration from initial velocity, final velocity, and time; from the two velocities and the distance; from initial velocity, distance, and time; or from net force and mass using Newton’s second law. Every result arrives in meters per second squared, feet per second squared, and g, with the working shown step by step. If what you actually need is the distance traveled while accelerating, the sister tool linked below is built for that job.
All four methods assume constant (uniform) acceleration over the interval. Real launches and braking vary second by second, so treat the answer as the average acceleration across the motion you entered.
Quick Answer
Key takeaways
- Acceleration is change in velocity divided by time: a = (v − u) ÷ t. It is a vector, so the sign carries direction: negative means slowing down.
- Four input sets solve the same quantity: velocities with time, velocities with distance, distance with time, and force with mass.
- The SI unit is m/s². Multiply by 3.28084 for ft/s², and divide by 9.80665 to express the result as a multiple of Earth gravity (g).
- Every method here assumes constant acceleration. For varying acceleration, the result is the average over the interval.
- Acceleration is not distance. If you need how far something travels while speeding up, use the acceleration distance calculator linked below.
How to use the Acceleration Calculator
Start with the Known values selector: it is the whole design of the tool. Choose the row that matches the numbers your problem actually gives you, fill in that panel, and press Calculate. The first panel also accepts velocities in km/h, mph, and ft/s, converting each to meters per second before dividing, so a 0 to 60 mph problem can be typed in as stated.
The result leads with acceleration in m/s², then restates it in ft/s² and in g, because different audiences think in different units: engineers in SI, drivers in g. Underneath, numbered steps replay the exact substitution the calculator made, which makes the card double as homework checking: if your hand answer differs, the step where the two diverge is the step to recheck.
Know the acceleration and want the motion instead? That is the reverse problem, and the acceleration distance calculator solves it: distance, final velocity, and time under a constant acceleration you supply. The two tools are a pair, and problems that give you force and mass connect onward through the brute force calculator, which turns mass and acceleration back into the force involved. Gravity is the everyday special case: a falling object accelerates at 1 g, which the free fall distance calculator applies to dropped objects.
The four formulas, step by step
Velocity and time: a = (v − u) ÷ t. The definition itself. For the pre-filled values: (27.8 − 0) ÷ 5 = 5.560 m/s². This panel also reports the distance covered, from average velocity times time: 13.90 × 5 = 69.50 m.
Velocity and distance: a = (v² − u²) ÷ 2d. The time-free kinematic equation, for problems that give a runway, a braking zone, or a track length instead of a stopwatch. Defaults: (20² − 0) ÷ (2 × 100) = 2.000 m/s².
Distance and time: a = 2(d − ut) ÷ t². The displacement equation s = ut + ½at² rearranged. Defaults: 2 × (100 − 0 × 10) ÷ 10² = 2.000 m/s².
Force and mass: a = F ÷ m. Newton's second law. Defaults: 300 N ÷ 50 kg = 6.000 m/s². One newton is defined as the force that accelerates one kilogram by one meter per second squared, which is why the units cancel so cleanly.
| Method | Pre-filled inputs | Acceleration | In ft/s² | In g |
|---|---|---|---|---|
| Velocity, time | 0 to 27.8 m/s in 5 s | 5.560 m/s² | 18.241 | 0.567 |
| Velocity, distance | 0 to 20 m/s over 100 m | 2.000 m/s² | 6.562 | 0.204 |
| Distance, time | 100 m in 10 s from rest | 2.000 m/s² | 6.562 | 0.204 |
| Force, mass | 300 N on 50 kg | 6.000 m/s² | 19.685 | 0.612 |
Notice the second and third rows agree. They describe the same motion (reaching 20 m/s exactly as 100 m passes, 10 seconds in) from two different sets of givens, which is the consistency check the whole kinematic family rests on. OpenStax derives all of these equations from the definitions of average velocity and acceleration in University Physics, Section 3.3, and combines them for constant-acceleration problems in Section 3.4.
What everyday accelerations look like
Two sign habits prevent most mistakes. First, braking is negative acceleration only when the final velocity is smaller than the initial one in the same direction: enter both speeds as positive magnitudes traveling the same way, and the calculator returns the negative sign for you. Second, keep directions consistent inside the force method: F must be the net force in the direction of motion after friction, or the acceleration will describe a push that never happens. Georgia State's HyperPhysics reference covers the same one-dimensional treatment under acceleration, and The Physics Classroom works through sign conventions in its lesson on acceleration.
What competing calculators miss
We checked the top-ranking acceleration tools before rebuilding this page, including the large generalist sites. They are strong, but each leaves a route out.
Winning move 1: four methods, not three. The best-known competitor offers velocity difference, distance traveled, and mass and force. It has no velocity-and-distance mode, so a problem that gives two speeds and a distance (the classic braking and runway setup) cannot be solved there directly. This card adds a = (v² − u²) ÷ 2d as a first-class panel.
Winning move 2: steps, not just an answer. Generalist tools return a number in a field. This calculator prints the substitution it performed, line by line, which is what students and anyone checking a result actually need.
Winning move 3: three unit systems on every result. Each answer arrives in m/s², ft/s², and g at once, instead of making you re-run the tool with different unit settings to get the g figure pilots and drivers quote.
Winning move 4: a clean split from the distance tool. Some sites merge acceleration and distance into one overloaded solver where the unknown keeps changing. Here acceleration is the only unknown, and distance problems route to the dedicated sister calculator, so each card stays simple and its examples stay checkable.
Frequently asked questions
It depends on what you know. From velocities and time: a = (v − u) ÷ t. From velocities and distance: a = (v² − u²) ÷ (2d). From distance and time: a = 2(d − ut) ÷ t². From force and mass: a = F ÷ m, Newton's second law. All four are in the selector at the top of the calculator.
The object is slowing down in its direction of travel: final velocity is smaller than initial velocity, so the change is negative. Braking from 27.8 m/s to rest in 5 seconds gives (0 − 27.8) ÷ 5 = −5.560 m/s². Negative acceleration is often called deceleration.
Divide by standard gravity, 9.80665 m/s². The pre-filled result, 5.560 m/s², is 5.560 ÷ 9.80665 = 0.567 g. The calculator shows the g figure on every result, alongside ft/s², which is m/s² multiplied by 3.28084.
In the velocity and time panel, each velocity has its own unit selector: m/s, km/h, mph, or ft/s, converted to m/s before the division. The distance-based panels take m/s and meters. A handy check: 27.8 m/s is about 100 km/h or 62 mph, which is why the pre-filled example reads like a 0 to 100 km/h sprint.
Yes. All four equations describe uniform acceleration, so for a real car launch or a braking event with a soft start, the answer is the average acceleration over the interval you entered. For most textbook, engineering-estimate, and comparison purposes, the average is the figure wanted.
Velocity is how fast position changes, measured in m/s. Acceleration is how fast velocity changes, measured in m/s²: an extra per second in the unit because it is a rate of a rate. A car cruising at a steady 27.8 m/s has high velocity and zero acceleration; the same car reaching that speed in 5 seconds has an acceleration of 5.560 m/s².
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References
- Khan Academy, "What is acceleration?" - the definition of acceleration as change in velocity over time, derived from velocity-time graphs, with the sign conventions for speeding up and slowing down. Khan Academy: What Is Acceleration?. Accessed October 2026.
- OpenStax, University Physics Volume 1, "3.3 Average and Instantaneous Acceleration" - average versus instantaneous acceleration and how each is computed from velocity data. OpenStax: Average and Instantaneous Acceleration. Accessed October 2026.
- OpenStax, University Physics Volume 1, "3.4 Motion with Constant Acceleration" - the kinematic equations, including v squared equals u squared plus 2as and s equals ut plus half a t squared. OpenStax: Motion with Constant Acceleration. Accessed October 2026.
- National Institute of Standards and Technology, "Standard acceleration of gravity" - the exact conventional value, 9.80665 m/s², used for every g conversion in this calculator. NIST: Standard Acceleration of Gravity. Accessed October 2026.
- Georgia State University, HyperPhysics, "Acceleration" - one-dimensional acceleration definitions and worked relationships between velocity, time, and distance. HyperPhysics: Acceleration. Accessed October 2026.
- The Physics Classroom, "Acceleration" (1-D Kinematics, Lesson 1) - direction and sign conventions for acceleration vectors, with everyday examples. The Physics Classroom: Acceleration. Accessed October 2026.