🚀 Free Physics Tool

Free Velocity Solver — Speed, Distance & Time Calculator

Solve any velocity, speed, distance or time problem instantly. Enter any two values and get the third — with full step-by-step working shown. Includes unit conversion for km/h, m/s, mph and more. No sign-up, completely free.

✓ Find Speed / Velocity ✓ Find Distance ✓ Find Time ✓ Unit Converter ✓ Acceleration Calculator ✓ Step-by-Step Solution

🚀

Velocity Solver — Select what you want to calculate

Speed (v) = Distance (d) ÷ Time (t)

Enter distance and time to calculate speed

Distance

Unit

Time

Unit

Speed vs Velocity: Speed is a scalar quantity (magnitude only). Velocity is a vector quantity (magnitude + direction). In most physics problems, the formula v = d/t applies to both when direction is fixed.

Distance (d) = Speed (v) × Time (t)

Enter speed and time to calculate distance

Speed

Unit

Time

Unit

Time (t) = Distance (d) ÷ Speed (v)

Enter distance and speed to calculate time

Distance

Unit

Speed

Unit

Convert any speed unit instantly — all results shown together

Enter a speed value and select its unit

Speed Value

From Unit

Common conversions: 1 km/h = 0.2778 m/s · 1 mph = 1.609 km/h · 1 knot = 1.852 km/h · 1 m/s = 3.6 km/h

Acceleration (a) = (Final Velocity − Initial Velocity) ÷ Time

Enter initial velocity, final velocity and time

Initial Velocity (u)

Final Velocity (v)

Unit

Time (seconds)

SUVAT equations: v = u + at · s = ut + ½at² · v² = u² + 2as · s = (u+v)/2 × t. These four equations cover all uniform acceleration problems in physics.

Step by Step

How to solve velocity, speed, distance and time problems

All speed, distance and time problems are based on one triangle — three variables, three formulas. Cover the variable you want to find, and the remaining two show how to calculate it.

S×T

Cover D → S × T | Cover S → D ÷ T | Cover T → D ÷ S

How to calculate speed

Divide the total distance traveled by the total time taken.

Speed = Distance ÷ Time (v = d / t)

Example: A car travels 120 km in 2 hours. What is its speed? Speed = 120 ÷ 2 = 60 km/h
In m/s: 60 ÷ 3.6 = 16.67 m/s

How to calculate distance

Multiply the speed by the total time of travel.

Distance = Speed × Time (d = v × t)

Example: A train moves at 80 km/h for 3.5 hours. How far does it travel? Distance = 80 × 3.5 = 280 km

How to calculate time

Divide the total distance by the speed.

Time = Distance ÷ Speed (t = d / v)

Example: A cyclist covers 45 km at 15 km/h. How long does it take? Time = 45 ÷ 15 = 3 hours

How to convert km/h to m/s

To convert kilometres per hour to metres per second, divide by 3.6.

m/s = km/h ÷ 3.6

Example: Convert 90 km/h to m/s 90 ÷ 3.6 = 25 m/s

How to convert m/s to km/h

To convert metres per second to kilometres per hour, multiply by 3.6.

km/h = m/s × 3.6

Example: Convert 20 m/s to km/h 20 × 3.6 = 72 km/h

Speed unit conversion table

km/h	m/s	mph	knots	ft/s
1	0.2778	0.6214	0.5400	0.9113
10	2.778	6.214	5.400	9.113
30	8.333	18.641	16.199	27.34
60	16.667	37.282	32.397	54.68
100	27.778	62.137	53.996	91.13
120	33.333	74.565	64.795	109.36

Physics Reference

Key velocity & motion formulas

Speed

v = d / t

Speed equals distance divided by time. The most fundamental motion equation.

Distance

d = v × t

Distance equals speed multiplied by time. Used to find how far an object travels.

Time

t = d / v

Time equals distance divided by speed. Used to find how long a journey takes.

Acceleration

a = (v−u) / t

Acceleration equals change in velocity divided by time. v = final, u = initial.

SUVAT — 1

v = u + at

Final velocity equals initial velocity plus acceleration times time.

SUVAT — 2

s = ut + ½at²

Displacement equals initial velocity times time plus half acceleration times time squared.

SUVAT — 3

v² = u² + 2as

Final velocity squared equals initial velocity squared plus 2 times acceleration times displacement.

Average Speed

v_avg = (u+v)/2

Average velocity equals the sum of initial and final velocities divided by 2.

Symbol	Quantity	SI Unit	Description
v	Velocity / Speed	m/s	Rate of change of position
u	Initial Velocity	m/s	Speed at the start of motion
a	Acceleration	m/s²	Rate of change of velocity
s / d	Displacement / Distance	m	Distance traveled in a direction
t	Time	s (seconds)	Duration of motion
g	Gravitational acceleration	9.81 m/s²	Free fall acceleration on Earth

Why Us

Why use this velocity solver?

⚡

Solve any variable

Find speed, distance, or time — enter any two values and get the third instantly with all unit conversions.

📐

Steps always shown

Every calculation comes with a full step-by-step breakdown so you understand the method for your physics exam.

🔄

All units supported

km/h, m/s, mph, knots, ft/s — convert between any speed unit instantly. All conversions shown at once.

🔓

100% free, no sign-up

No account, no email, no hidden limits. Works on any device — built for physics students who need fast answers.

FAQ

Frequently asked questions about velocity and speed

The formula for speed is: Speed = Distance ÷ Time (v = d/t). To find distance, use Distance = Speed × Time. To find time, use Time = Distance ÷ Speed. These three formulas form the speed-distance-time triangle used in all basic motion problems.

To convert km/h to m/s, divide by 3.6. Formula: m/s = km/h ÷ 3.6. Example: 90 km/h ÷ 3.6 = 25 m/s. The reason is that 1 km = 1000 m and 1 hour = 3600 seconds, so 1 km/h = 1000/3600 = 1/3.6 m/s.

To convert m/s to km/h, multiply by 3.6. Formula: km/h = m/s × 3.6. Example: 25 m/s × 3.6 = 90 km/h. This is the reverse of the km/h to m/s conversion and is frequently asked in physics exams.

Speed is a scalar quantity — it only has magnitude (e.g. 60 km/h). Velocity is a vector quantity — it has both magnitude and direction (e.g. 60 km/h north). In straight-line motion problems with fixed direction, the two terms are often used interchangeably. The mathematical formulas v = d/t and v = d/t apply to both.

SUVAT equations describe uniformly accelerated motion. The four equations are: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as, (4) s = (u+v)/2 × t. Where s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time. These are used in all A-Level and university physics problems involving constant acceleration.

Acceleration = (Final Velocity − Initial Velocity) ÷ Time. Formula: a = (v − u) / t. Example: A car accelerates from 0 to 30 m/s in 10 seconds. Acceleration = (30 − 0) ÷ 10 = 3 m/s². The SI unit for acceleration is metres per second squared (m/s²).

To convert km/h to mph, divide by 1.60934. Formula: mph = km/h ÷ 1.60934. Example: 100 km/h ÷ 1.60934 = 62.14 mph. To convert mph to km/h, multiply by 1.60934.

Average speed is the total distance traveled divided by the total time taken. Formula: Average Speed = Total Distance ÷ Total Time. Note: average speed is NOT simply the average of two speeds, unless the time spent at each speed is equal. If equal distances are covered at different speeds, use the harmonic mean: 2v₁v₂/(v₁+v₂).

The speed of light in a vacuum is approximately 299,792,458 m/s, which equals about 1,079,252,849 km/h (roughly 1.08 billion km/h). In miles per hour, that is approximately 670,616,629 mph. This is the universal speed limit — no object with mass can reach or exceed it.

More Free Tools