What is the difference between acceleration and velocity?

Velocity is the rate of change of position and includes direction. Acceleration is the rate of change of velocity, so it can reflect a change in speed or direction. Constant velocity means zero acceleration.

Can acceleration be negative?

Yes. Negative acceleration means velocity changes in the negative direction of the chosen axis. Whether speed rises or falls depends on the velocity direction.

What is the acceleration due to gravity?

On Earth, gravity causes objects to accelerate downward at approximately 9.8 m/s² (or 32.2 ft/s²). This means that in free fall, an object's velocity increases by 9.8 m/s every second.

How do I convert between metric and imperial units?

For acceleration: 1 m/s² = 3.28 ft/s². For velocity: 1 m/s = 2.237 mph. The calculator handles these conversions automatically when you select your preferred unit system.

Acceleration Calculator

Calculate signed acceleration, signed displacement, and average velocity from two signed velocities and positive time, assuming constant acceleration.

Method and source check

Last checked: Sep 30, 2026

Automated source and implementation review, including worked examples and documented numerical limits. This review does not provide professional advice or specialist approval.

Method

Calculate signed acceleration from velocity change over positive time. Under constant acceleration, calculate signed displacement as average velocity × time. Convert mph inputs to ft/s before imperial acceleration and displacement.

a = (v_f − v_i) / t

displacement = ((v_i + v_f) / 2) × t

Variables and units

v_i,v_f: initial/final signed velocity, m/s or mph
t: elapsed seconds
a: m/s² or ft/s²
displacement: signed meters or feet

Worked example

0 to 60mph over 10s gives 8.8ft/s² and 440ft displacement, with 30mph average velocity.

Limitations

Acceleration, signed displacement, and average velocity retain floating-point precision; the UI displays up to six significant digits.

The displacement formula assumes constant acceleration on one signed axis. Signed displacement is not total path distance.
Unsupported derived numerical ranges are rejected with a localized error on a visible form field; the calculations use floating-point arithmetic.
0→10m/s over2s → 5m/s², 10m displacement
0→60mph over10s → 8.8ft/s², 440ft displacement
−10→−5m/s over1s → positive 5m/s² and −7.5m displacement

Sources

Table of Contents

How to Use

Choose metric velocities in m/s or imperial velocities in mph.
Enter signed initial and final velocities and a time greater than zero in seconds.
Read acceleration, signed displacement, and average velocity in the displayed units.
Use the sign to read direction along the chosen axis; signed displacement can be negative.

Choose metric velocities in m/s or imperial velocities in mph

Enter signed initial and final velocities and a time greater than zero in seconds. Acceleration is the rate at which velocity changes over time. It's a fundamental concept in physics that describes how quickly an object speeds up, slows down, or changes direction.

The basic formula for acceleration is: a = (v_f - v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is time.

Method source: OpenStax, Rice University. https://openstax.org/books/physics/pages/3-1-acceleration

Acceleration and signed displacement

Assuming constant acceleration, a = (final velocity − initial velocity) ÷ time, average velocity = (initial + final velocity) ÷ 2, and signed displacement = average velocity × time. Imperial mph inputs are converted to ft/s before ft/s² and feet are calculated.

Reading the sign

A positive acceleration means velocity changes in the positive axis direction; a negative acceleration means change in the negative direction. Either sign can accompany increasing or decreasing speed, depending on the velocity direction.

Check the motion model

The calculated displacement uses the average of the initial and final signed velocities. Use it only when constant acceleration is a suitable assumption for the interval.

Worked example

From 0 to 10 m/s in 2 s, constant acceleration is 5 m/s² and signed displacement is 10 m. A negative displacement indicates direction on the chosen axis.

Frequently Asked Questions

What is the difference between acceleration and velocity?: Velocity is the rate of change of position and includes direction. Acceleration is the rate of change of velocity, so it can reflect a change in speed or direction. Constant velocity means zero acceleration.
Can acceleration be negative?: Yes. Negative acceleration means velocity changes in the negative direction of the chosen axis. Whether speed rises or falls depends on the velocity direction.
What is the acceleration due to gravity?: On Earth, gravity causes objects to accelerate downward at approximately 9.8 m/s² (or 32.2 ft/s²). This means that in free fall, an object's velocity increases by 9.8 m/s every second.
How do I convert between metric and imperial units?: For acceleration: 1 m/s² = 3.28 ft/s². For velocity: 1 m/s = 2.237 mph. The calculator handles these conversions automatically when you select your preferred unit system.

Related Calculators

Science

Acceleration Calculator

Method

Variables and units

Worked example

Limitations

Sources

How to Use

Choose metric velocities in m/s or imperial velocities in mph

Acceleration and signed displacement

Reading the sign

Check the motion model

Worked example

Frequently Asked Questions

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