Acceleration Calculator

Q: What is the acceleration due to gravity on Earth?

The standard value is g = 9.80665 m/s² (exactly, by definition of the standard). In practice, g varies slightly with latitude and altitude: 9.78 m/s² at the equator and 9.83 m/s² at the poles. For most physics problems and this calculator, g = 9.8 m/s² is used. On the Moon g is about 1.62 m/s², on Mars about 3.72 m/s².

Q: Can acceleration be negative?

Yes. A negative acceleration value (also called deceleration or retardation) means the object is slowing down (when it is already moving in the positive direction) or speeding up in the negative direction. The sign of acceleration is determined by the direction you define as positive. There is nothing physically special about a negative value, which is a sign convention.

Solve for acceleration, final velocity, or time using the first kinematic equation.

Initial Velocity (u) m/s

m/s

Final Velocity (v) m/s

m/s

Time (t) s

Initial Velocity (u) m/s

m/s

Acceleration (a) m/s²

m/s²

Time (t) s

Initial Velocity (u) m/s

m/s

Final Velocity (v) m/s

m/s

Acceleration (a) m/s²

m/s²

Acceleration

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Formula Used

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Acceleration

m/s²

—

g-force

—

ft/s²

—

Kinematics Summary

Initial Velocity (u)

—

Final Velocity (v)

—

Time (t)

—

Displacement (m)

—

Displacement (ft)

—

🏎️ What is Acceleration?

Acceleration is the rate at which an object's velocity changes over time. It is one of the four fundamental SUVAT variables in classical mechanics, alongside displacement (s), initial velocity (u), final velocity (v), and time (t). The defining formula is a = (v - u) / t, which states that acceleration equals the change in velocity divided by the time taken for that change. In SI units, acceleration is measured in metres per second squared (m/s²).

Acceleration appears in countless real-world scenarios. A car pressing on the accelerator pedal increases its velocity, experiencing positive acceleration. A car applying its brakes decreases velocity, experiencing negative acceleration (also called deceleration or retardation). A freely falling object near Earth's surface accelerates downward at approximately 9.8 m/s² due to gravity, gaining roughly 35 km/h of speed for every second it falls. A rocket at liftoff might experience 3 g of acceleration, while a roller coaster car can subject riders to 4 to 5 g through tight loops.

A common misconception is that a fast-moving object must be accelerating. This is wrong: a car cruising at constant 100 km/h has zero acceleration. Acceleration is about the change in velocity, not the velocity itself. Another misconception is that deceleration is a physically different concept. In physics, it is simply negative acceleration and uses exactly the same formula with the same sign conventions.

This calculator uses the first kinematic equation and assumes uniform (constant) acceleration throughout the time interval. It can solve for any one of the three variables, acceleration, final velocity, or time, when the other two are known. It also computes displacement using s = ut + 0.5at², giving you a complete kinematic picture from a single calculation. Results are displayed in m/s², g-force, and ft/s² simultaneously, eliminating unit conversion steps.

📐 Formula

a = (v − u) ÷ t

a = acceleration (m/s²)

v = final velocity (m/s)

u = initial velocity (m/s)

t = time (s)

Example: u = 0 m/s, v = 27.78 m/s, t = 8 s → a = 27.78 / 8 = 3.47 m/s²

This is the first of the five SUVAT kinematic equations. The three rearrangements are:

v = u + at

Find final velocity when u, a, and t are known.

Example: u = 0, a = 9.8 m/s², t = 3 s → v = 29.4 m/s

t = (v − u) ÷ a

Find time when u, v, and a are known.

Example: u = 0, v = 50 m/s, a = 5 m/s² → t = 10 s

Displacement during the acceleration period (also computed automatically):

s = ut + ½at²

s = displacement (m)

Assumes constant acceleration over the interval.

📖 How to Use This Calculator

Steps

Select what you want to find: choose Find Acceleration, Find Final Velocity, or Find Time from the tabs at the top of the widget.

Enter the known values: type initial velocity and final velocity in m/s, time in seconds, or acceleration in m/s² depending on the mode. Use negative values for deceleration or reverse motion.

Click Calculate. The result appears instantly in the panel below, showing the primary answer, acceleration in three unit systems, and displacement.

Read all results. The kinematics summary shows u, v, a, t, and displacement in both metres and feet. No manual conversion needed.

Use the formula row. The displayed equation with substituted values confirms the exact calculation, ideal for checking exam workings.

💡 Example Calculations

Example 1: Car accelerating from rest to 100 km/h

A car starts from rest and reaches 100 km/h in 8 seconds. What is its acceleration?

Convert: 100 km/h = 100 / 3.6 = 27.78 m/s. Initial velocity u = 0 m/s (starts from rest). Time t = 8 s.

Apply a = (v - u) / t = (27.78 - 0) / 8 = 3.47 m/s².

In g-force: 3.47 / 9.80665 = 0.354 g. Displacement: s = 0 x 8 + 0.5 x 3.47 x 64 = 111.1 m.

a = 3.47 m/s² (0.354 g), distance covered: 111.1 m

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Example 2: Object in free fall

A ball is dropped from rest. What is its velocity after 3 seconds of free fall?

Initial velocity u = 0 m/s (dropped from rest). Acceleration a = 9.8 m/s² (gravity). Time t = 3 s.

Apply v = u + at = 0 + 9.8 x 3 = 29.4 m/s.

Displacement: s = 0 x 3 + 0.5 x 9.8 x 9 = 44.1 m. The ball has fallen approximately 44 m.

v = 29.4 m/s (105.8 km/h) after falling 44.1 m

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Example 3: Emergency braking

A car travelling at 30 m/s brakes to a stop with a deceleration of 6 m/s². How long does it take?

Initial velocity u = 30 m/s. Final velocity v = 0 m/s (stops). Acceleration a = -6 m/s² (deceleration).

Apply t = (v - u) / a = (0 - 30) / (-6) = 5 s.

Braking distance: s = 30 x 5 + 0.5 x (-6) x 25 = 150 - 75 = 75 m. This is the minimum stopping distance at 108 km/h with 6 m/s² braking.

t = 5 s, braking distance: 75 m

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Example 4: Rocket at liftoff

A rocket lifts off from rest and accelerates at 25 m/s² for 10 seconds. What is its final velocity?

Initial velocity u = 0 m/s. Acceleration a = 25 m/s². Time t = 10 s.

Apply v = u + at = 0 + 25 x 10 = 250 m/s = 900 km/h.

Displacement: s = 0 + 0.5 x 25 x 100 = 1,250 m = 1.25 km altitude gained. G-force: 25 / 9.80665 = 2.55 g.

v = 250 m/s (900 km/h), altitude gained: 1.25 km, g-force: 2.55 g

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❓ Frequently Asked Questions

What is the formula for acceleration?+

The standard formula is a = (v - u) / t, where a is acceleration in m/s², v is final velocity in m/s, u is initial velocity in m/s, and t is time in seconds. This can be rearranged to find final velocity (v = u + at) or time (t = (v - u) / a). It is the first of the five SUVAT kinematic equations for uniform acceleration.

What is the SI unit of acceleration?+

The SI unit of acceleration is metres per second squared (m/s²). This means the velocity changes by that many m/s every second. Acceleration is also commonly expressed in g (multiples of standard gravity, 9.80665 m/s²) or ft/s² in some engineering contexts. A car accelerating at 3 m/s² gains 3 m/s of speed every second.

What is the difference between acceleration and deceleration?+

Deceleration is simply negative acceleration, which means the object is slowing down. If a car brakes from 20 m/s to 0 m/s in 4 seconds, the acceleration is (0 - 20) / 4 = -5 m/s². There is no separate formula for deceleration; you just get a negative result. Speed decreases when acceleration opposes the direction of motion.

How many g-forces is 1 m/s²?+

1 m/s² = 1 / 9.80665 g, which is approximately 0.102 g. Conversely, 1 g = 9.80665 m/s². The g unit is useful in aviation and motorsport because humans perceive acceleration as a fraction of gravity. A jet fighter pulling 6 g is accelerating at 6 x 9.80665 = 58.84 m/s².

What is uniform acceleration?+

Uniform (constant) acceleration means the rate of change of velocity is the same at every instant. All SUVAT equations, including a = (v - u) / t, assume uniform acceleration. Free fall near Earth's surface (ignoring air resistance) is the classic example: every object accelerates at g = 9.8 m/s² regardless of mass. Non-uniform acceleration requires calculus.

How do I calculate acceleration from distance and time?+

If you know distance (s), initial velocity (u), and time (t), use the SUVAT equation: a = 2(s - ut) / t². If the object starts from rest (u = 0), this simplifies to a = 2s / t². For example, a car starting from rest covers 50 m in 5 s: a = 2 x 50 / 25 = 4 m/s². The Kinematics Calculator handles all five SUVAT equations simultaneously.

What is the acceleration due to gravity on Earth?+

The standard value is g = 9.80665 m/s² exactly, by international definition. In practice g varies slightly with latitude and altitude: 9.78 m/s² at the equator and 9.83 m/s² at the poles. For most physics problems g = 9.8 m/s² is used. On the Moon g is about 1.62 m/s², on Mars about 3.72 m/s².

How is acceleration related to force?+

By Newton's second law, F = ma, so a = F / m. A net force of 100 N acting on a 20 kg object produces an acceleration of 5 m/s². This formula gives instantaneous acceleration for a given net force and does not require uniform acceleration. For force-based calculations, use the Force Calculator at /science/physics/force-calculator/.

Can acceleration be negative?+

Yes. A negative acceleration value means the object is slowing down (when moving in the positive direction) or speeding up in the negative direction. The sign of acceleration is determined by the direction you define as positive. There is nothing physically special about a negative value, which is a sign convention that follows from the choice of coordinate system.

What is the difference between average and instantaneous acceleration?+

Average acceleration = (v - u) / t over a time interval. Instantaneous acceleration is the limit of average acceleration as the time interval approaches zero, equal to the derivative dv/dt. For uniform acceleration they are equal. For variable acceleration (e.g. a car engine with varying power output), only instantaneous acceleration equals dv/dt at each moment.

How far does an object travel while accelerating?+

Use the SUVAT equation s = ut + 0.5at². For a car starting from rest (u = 0) and accelerating at 4 m/s² for 5 seconds: s = 0 + 0.5 x 4 x 25 = 50 m. This calculator shows displacement automatically for every calculation. Alternatively, use s = (u + v) / 2 x t if you know initial and final velocities rather than acceleration.

What acceleration is needed to reach 100 km/h in 8 seconds?+

100 km/h = 27.78 m/s. Using a = (v - u) / t with u = 0, v = 27.78 m/s, t = 8 s: a = 27.78 / 8 = 3.47 m/s² (0.354 g). Most family cars produce 2.5 to 4 m/s² of acceleration. Sports cars can exceed 10 m/s² (about 1 g), and top-fuel dragsters can reach 40 m/s² (about 4 g).

Tags: Acceleration Calculator Acceleration Formula A = (V-U)/T Kinematic Equations Physics Calculator G-Force Calculator Final Velocity Calculator Calculator Formula Free Online

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📌 Quick Tips

💡Standard gravity (g) is 9.80665 m/s². Free-falling objects near Earth's surface accelerate at approximately 9.8 m/s² downward (ignoring air resistance). Use acceleration = 9.8 m/s² and initial velocity = 0 to model free fall.

💡Deceleration is simply negative acceleration. If a car slows from 30 m/s to 0 in 6 s, the acceleration is (0 - 30) / 6 = -5 m/s². The negative sign means the velocity is decreasing.

💡1 g = 9.80665 m/s². Fighter pilots typically experience 4-9 g during manoeuvres. Formula One drivers experience up to 6 g under braking. A sneeze produces about 3 g.

💡The displacement formula s = ut + 0.5at² assumes constant (uniform) acceleration. For varying acceleration, you need calculus or numerical integration. This calculator is valid for constant-acceleration scenarios.

💡To find acceleration using Force and mass, use a = F / m (Newton's second law). The Force Calculator at /science/physics/force-calculator/ is the right tool for that approach.