Velocity Calculator | Speed & Time
Calculate velocity, distance, or time using v = d/t.
Formula Mode
Solve For
What Is the Velocity Calculator | Speed & Time?
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.
Formula
v = d / tv = v₀ + a·tv² = v₀² + 2a·dd = v₀·t + ½a·t²How 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.
Example Calculation
Example 1, Car trip
A car travels 250 km in 2.5 hours. What is its average speed?
Example 2, Braking car
A car at 30 m/s decelerates at −5 m/s². What is its speed after 4 seconds?
Example 3, Kinetic energy
A 1200 kg car at 100 km/h (27.78 m/s) has kinetic energy:
Understanding Velocity | Speed & Time
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.
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).