Physics

Velocity Calculator | Speed & Time

Calculate velocity, distance, or time using v = d/t.

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Formula Mode

Solve For

Distance

Time

Overview

What Is the Velocity Calculator?

The Velocity Calculator solves for any variable in the fundamental motion equations, speed, distance, time, or acceleration. Switch between Basic mode (v = d/t with unit conversion for speed, distance, and time) and Kinematic mode (v = v₀ + at with all three SUVAT equations displayed). Results include automatic conversion to m/s, km/h, mph, ft/s, and Mach number, plus optional kinetic energy if you supply a mass.

Live calculations update as you type. All common speed, distance, and time units are supported with automatic conversion at calculation time.

How it works

Velocity Calculator Formula and Method

Basicv = d / tSpeed from distance and time

Kinematicv = v₀ + a·tFinal velocity from initial + acceleration

Kinematic 2v² = v₀² + 2a·dFinal velocity without time

Kinematic 3d = v₀·t + ½a·t²Displacement formula

Instructions

How to Use

Basic Mode, v = d / t

›Choose "Solve for", Velocity, Distance, or Time.
›Enter the known values and select units for each (e.g. km for distance, hours for time).
›Click Calculate, results appear in all speed units plus Mach number.
›Optionally enter a mass to see kinetic energy.

Kinematic Mode, v = v₀ + at

›Enter initial velocity v₀, acceleration a, and time t.
›All three kinematic equations are solved and displayed simultaneously.
›Results include final velocity, displacement, and average velocity.

Real example

Velocity Calculator Example

Example 1, Car trip

A car travels 250 km in 2.5 hours. What is its average speed?

v = 250 km ÷ 2.5 h = 100 km/h (= 62.14 mph = 27.78 m/s)

Example 2, Braking car

A car at 30 m/s decelerates at −5 m/s². What is its speed after 4 seconds?

v = 30 + (−5 × 4) = 30 − 20 = 10 m/s

Example 3, Kinetic energy

A 1200 kg car at 100 km/h (27.78 m/s) has kinetic energy:

KE = ½ × 1200 × 27.78² = 462,963 J ≈ 463 kJ

Guide

Understanding Velocity

What Is Velocity?

Velocity is the rate of change of position with respect to time. In everyday language we often use "speed" and "velocity" interchangeably, but physics draws a clear distinction: speed is a scalar (magnitude only), while velocity is a vector(magnitude + direction). The fundamental relationship is:

›v = d / t, average speed over a distance d in time t.
›v = v₀ + at, final velocity under constant acceleration a starting from v₀.
›The SI unit of velocity is metres per second (m/s).

Speed Unit Conversion Reference

Common speed conversions used in engineering, aviation, and everyday life:

m/s	km/h	mph	ft/s	knots	Mach	Context
1	3.6	2.237	3.281	1.944	0.00292	SI base unit
27.78	100	62.14	91.13	53.99	0.081	Highway speed
44.70	160.93	100	146.67	86.90	0.130	100 mph reference
270.28	972.9	604.5	886.9	527.3	0.787	Transatlantic cruising
343	1,235	767.3	1,125	667.6	1.000	Speed of sound (20°C)
8,050	28,980	18,000	26,410	15,660	23.47	Low Earth orbit (LEO)
299,792,458	1,079,253,000	670,616,629	983,571,056	582,749,918	874,030	Speed of light

The Kinematic Equations

For motion with constant acceleration, the SUVAT equations link five variables: displacement (s), initial velocity (v₀), final velocity (v), acceleration (a), and time (t). Any three known values determine the other two.

›These equations assume constant (uniform) acceleration, a straight-line relationship between velocity and time.
›In the real world, acceleration is rarely constant: use numerical integration for variable-acceleration problems.
›Projectile motion uses these equations separately for horizontal (a = 0) and vertical (a = −g = −9.81 m/s²) components.

Practical Applications

›Traffic safety, Stopping distance scales with v² (not v), so doubling speed quadruples stopping distance.
›Fuel efficiency, Aerodynamic drag force ∝ v², making highway driving exponentially more fuel-intensive than city driving.
›Orbital mechanics, The ISS orbits at ~7,660 m/s (27,580 km/h) to maintain low Earth orbit.
›Ballistics, Muzzle velocity determines bullet trajectory, energy transfer, and effective range.
›Relativity, At speeds above ~10% of c (30,000 km/s), Newtonian mechanics breaks down and special relativity must be used.

Answers

Frequently Asked Questions

What is the difference between speed and velocity?

Speed is a scalar quantity, it has magnitude only (e.g. 60 km/h). Velocity is a vector, it has both magnitude and direction (e.g. 60 km/h north). This calculator computes speed (magnitude of velocity) for basic mode. In kinematic mode, positive/negative values indicate direction along the chosen axis.

How do I convert km/h to m/s?

Divide by 3.6: m/s = km/h ÷ 3.6. For example, 90 km/h ÷ 3.6 = 25 m/s. To convert m/s to km/h, multiply by 3.6. This calculator handles all unit conversions automatically.

What are the five SUVAT equations?

›v = v₀ + at (velocity, no displacement)
›s = v₀t + ½at² (displacement, no final velocity)
›s = vt − ½at² (displacement, no initial velocity)
›v² = v₀² + 2as (velocity, no time)
›s = ½(v₀ + v)t (displacement using average velocity)

What is Mach number?

Mach number is the ratio of an object's speed to the speed of sound in the surrounding medium. Mach 1 = 343 m/s (1,235 km/h) at 20°C in air. Mach numbers below 1 are subsonic, above 1 are supersonic, and above 5 are hypersonic.

What is the fastest speed ever recorded for a human-made object?

The Parker Solar Probe reached approximately 692,000 km/h (430,000 mph) in November 2021, about 0.064% of the speed of light. This translates to roughly Mach 560 in air (though the probe operates in space where sound speed is not applicable).

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