Velocity Calculator
Calculate velocity, distance, or time using kinematic equations. Find average and final velocity with acceleration, initial velocity, and time inputs.
Average Velocity
10.0000 m/s
Calculation
Average velocity = 100.00 m / 10.00 s
= 10.0000 m/s
Velocity Conversions
10.00 m/s
36.00 km/h
22.37 mph
19.44 knots
Common Speed References
- β’ Walking: 1.4 m/s (5 km/h)
- β’ Running: 3-6 m/s (10-20 km/h)
- β’ Cycling: 5-10 m/s (18-36 km/h)
- β’ Highway driving: 28-33 m/s (100-120 km/h)
- β’ Speed of sound: 343 m/s (1,235 km/h)
Related Calculators
About This Calculator
Velocity measures how fast an object moves in a specific direction. Unlike speed (which is just magnitude), velocity is a vector quantity with both magnitude and direction. This calculator helps you solve kinematics problems involving velocity, distance, time, and acceleration.
What is Velocity? Velocity is the rate of change of position with respect to time. The basic formula v = d/t gives average velocity, while kinematic equations handle cases with constant acceleration.
Key Equations:
- v = d/t (average velocity)
- v = vβ + at (final velocity with acceleration)
- d = vβt + Β½atΒ² (distance with acceleration)
- vΒ² = vβΒ² + 2ad (velocity-distance relation)
Velocity vs. Speed:
- Speed: How fast (scalar, always positive)
- Velocity: How fast and in what direction (vector)
Common Applications:
- Travel time calculations
- Physics problem-solving
- Vehicle dynamics
- Sports analysis
- Engineering design
This calculator handles multiple kinematic equations. For acceleration problems, see our Acceleration Calculator. For force analysis, see our Force Calculator.
How to Use the Velocity Calculator
- 1Select what you want to calculate: velocity, distance, or time.
- 2For average velocity, enter distance and time.
- 3For final velocity, enter initial velocity, acceleration, and time.
- 4For distance, enter initial velocity, acceleration, and time.
- 5For time, enter distance, initial velocity, and acceleration.
- 6Select appropriate units for each input.
- 7Review the calculated result with its formula.
- 8Check the unit conversions for different systems.
- 9Compare with reference values for context.
- 10Apply to real-world motion problems.
Kinematic Equations
The four key equations for motion with constant acceleration.
The Four Equations
1. v = vβ + at Final velocity from initial velocity and acceleration
2. d = vβt + Β½atΒ² Displacement from initial velocity and acceleration
3. vΒ² = vβΒ² + 2ad Relates velocity to displacement (no time)
4. d = Β½(vβ + v)t Displacement from average velocity
Variable Definitions
- v = final velocity
- vβ = initial velocity
- a = acceleration
- t = time
- d = displacement
Choosing the Right Equation
| Known | Unknown | Use |
|---|---|---|
| vβ, a, t | v | v = vβ + at |
| vβ, a, t | d | d = vβt + Β½atΒ² |
| vβ, a, d | v | vΒ² = vβΒ² + 2ad |
| vβ, v, t | d | d = Β½(vβ + v)t |
| vβ, v, d | a | vΒ² = vβΒ² + 2ad |
| vβ, v, a | t | v = vβ + at |
Velocity vs. Speed
Understanding the important distinction.
Speed (Scalar)
- Magnitude only
- Always positive or zero
- "How fast"
- Example: 60 mph
Velocity (Vector)
- Magnitude AND direction
- Can be positive, negative, or zero
- "How fast and which way"
- Example: 60 mph north
Average vs. Instantaneous
Average Velocity: v_avg = total displacement / total time
Instantaneous Velocity: v = lim(Ξtβ0) Ξx/Ξt = dx/dt
The velocity at a specific moment.
Example: Round Trip
Drive 100 km north, then 100 km south.
- Total distance: 200 km
- Total displacement: 0 km
- Average speed: 200 km / (total time)
- Average velocity: 0 (returned to start)
Direction Conventions
- Typically: right/up = positive
- Left/down = negative
- Choose a convention and be consistent
Unit Conversions
Converting between velocity units.
Common Velocity Units
| Unit | m/s | km/h | mph |
|---|---|---|---|
| 1 m/s | 1 | 3.6 | 2.237 |
| 1 km/h | 0.278 | 1 | 0.621 |
| 1 mph | 0.447 | 1.609 | 1 |
| 1 ft/s | 0.305 | 1.097 | 0.682 |
| 1 knot | 0.514 | 1.852 | 1.151 |
Quick Conversions
m/s to km/h: multiply by 3.6 km/h to m/s: divide by 3.6 mph to km/h: multiply by 1.609 km/h to mph: divide by 1.609
Distance Units
| Unit | Meters |
|---|---|
| 1 km | 1,000 m |
| 1 mile | 1,609.34 m |
| 1 yard | 0.9144 m |
| 1 foot | 0.3048 m |
Time Conversions
- 1 hour = 3,600 seconds
- 1 minute = 60 seconds
- 1 day = 86,400 seconds
Common Applications
Real-world velocity calculations.
Travel Planning
Problem: How long to drive 300 km at 100 km/h? t = d/v = 300/100 = 3 hours
Problem: Average speed for 4-hour trip covering 350 km? v = d/t = 350/4 = 87.5 km/h
Vehicle Dynamics
0-60 mph (0-26.8 m/s) in 5 seconds: a = Ξv/t = 26.8/5 = 5.36 m/sΒ² (about 0.55 g)
Braking distance from 100 km/h (27.8 m/s): With a = -8 m/sΒ²: d = vΒ²/(2|a|) = 27.8Β²/16 = 48.3 m
Sports
100m sprint (10 seconds): Average velocity = 100/10 = 10 m/s (36 km/h)
Marathon (42.195 km in 2 hours): Average velocity = 42.195/2 = 21.1 km/h (5.86 m/s)
Reference Velocities
| Object/Activity | Velocity |
|---|---|
| Walking | 1.4 m/s (5 km/h) |
| Usain Bolt (max) | 12.4 m/s (44.7 km/h) |
| Cheetah | 30 m/s (108 km/h) |
| Highway car | 33 m/s (120 km/h) |
| Commercial jet | 250 m/s (900 km/h) |
| Sound (air) | 343 m/s (1,235 km/h) |
| Earth orbit | 7,900 m/s (28,440 km/h) |
| Light | 3Γ10βΈ m/s |
Motion Graphs
Interpreting position, velocity, and acceleration graphs.
Position-Time Graph
- Slope = velocity
- Straight line = constant velocity
- Curved line = changing velocity (acceleration)
- Horizontal line = stationary
Velocity-Time Graph
- Slope = acceleration
- Area under curve = displacement
- Straight line = constant acceleration
- Horizontal line = constant velocity
Acceleration-Time Graph
- Area under curve = change in velocity
- Horizontal line = constant acceleration
- Zero line = constant velocity
Reading Graphs
From position-time:
- Steep slope = fast
- Negative slope = moving backward
- Zero slope = stopped
From velocity-time:
- Above x-axis = moving forward
- Below x-axis = moving backward
- Crossing x-axis = changing direction
- Slope = acceleration
Area Calculations
For velocity-time graphs:
- Rectangle: area = base Γ height
- Triangle: area = Β½ Γ base Γ height
- Trapezoid: area = Β½(sum of parallel sides) Γ height
Problem-Solving Strategies
Systematic approach to kinematics problems.
Step-by-Step Method
- Read carefully - identify what's given and what's asked
- Draw a diagram - sketch the situation
- Choose coordinates - define positive direction
- List known quantities with units
- Identify unknown quantity
- Select equation based on knowns/unknown
- Solve algebraically first, then substitute
- Check units and reasonableness
Common Mistakes
Sign errors:
- Forgetting acceleration due to gravity is negative (for upward positive)
- Mixing up direction conventions
Unit errors:
- Mixing m/s with km/h
- Using minutes instead of seconds
Equation selection:
- Using v = d/t when acceleration exists
- Forgetting initial velocity
Example Problem
A car accelerates from 20 m/s to 30 m/s over 100 m. Find time.
Given: vβ = 20 m/s, v = 30 m/s, d = 100 m Find: t
Solution: Using d = Β½(vβ + v)t: 100 = Β½(20 + 30)t 100 = 25t t = 4 seconds
Check: Average velocity = 25 m/s, distance = 25 Γ 4 = 100 m β
Pro Tips
- π‘Always define your positive direction before solving.
- π‘Use v = d/t for average velocity; kinematic equations for acceleration.
- π‘Check units at every step - they should cancel correctly.
- π‘Negative velocity means motion opposite to positive direction.
- π‘km/h to m/s: divide by 3.6; m/s to km/h: multiply by 3.6.
- π‘Draw a diagram for complex problems.
- π‘List knowns and unknowns before selecting an equation.
- π‘For constant acceleration, choose the equation missing the unknown you don't need.
- π‘Speed of sound β 343 m/s β 1,235 km/h (Mach 1).
- π‘Average velocity = total displacement / total time.
- π‘The slope of position-time graph = velocity.
- π‘The area under velocity-time graph = displacement.
Frequently Asked Questions
Speed is scalar (magnitude only) - how fast you're going. Velocity is a vector (magnitude and direction) - how fast and which way. If you drive in a circle and return to start, your average speed is positive but average velocity is zero because displacement is zero.
