Calculation
Ek = ½ · m · v²
Speed enters quadratically: doubling speed gives four times the energy.
Ek = ½mv²
Kinetic Energy Calculator
Speed enters quadratically: doubling speed gives four times the energy.
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Result
Select a target and calculate.
Understand the inputs
- Kinetic energy Ek — The energy of the body's translational (straight-line) motion. Since v enters squared, doubling the speed quadruples the energy rather than merely doubling it.
- Mass m — The total moving mass. Source: weigh it, or take it from a drawing/parts list; for vehicles include payload and occupants if they travel along with it.
- Speed v — The magnitude of the speed (direction not needed) at the moment considered. Source: a speedometer, a speed measurement, or computed from v = s/t.
Example
100 kg at 15.81 m/s have about 12.5 kJ.
Assumptions and limits
Point mass or pure translation; rotation is excluded.
Understand Kinetic Energy Calculator
This calculator finds the missing quantity among kinetic energy Ek, mass m and speed v from the other two. It shows why speed enters quadratically — a fact that is routinely underestimated when judging impact energy and stopping distance in road traffic.
What does this quantity describe?
The kinetic energy of a body is the energy stored in its motion: Ek = ½·m·v². Unlike a linear relationship, doubling the speed does not double the energy — it quadruples it.
This shows up clearly on the road: doubling a vehicle's speed from 30 to 60 km/h increases its kinetic energy — and, at roughly constant braking force, its stopping distance — to about four times the original value. That is why even moderate speeding disproportionately increases crash severity.
Formula and variables
Ek = ½ · m · v²
Ek = ½ · m · v²m = 2 · Ek / v²v = √(2 · Ek / m)
| Symbol / input | Meaning |
|---|---|
| Kinetic energy Ek | The energy of the body's translational (straight-line) motion. Since v enters squared, doubling the speed quadruples the energy rather than merely doubling it. |
| Mass m | The total moving mass. Source: weigh it, or take it from a drawing/parts list; for vehicles include payload and occupants if they travel along with it. |
| Speed v | The magnitude of the speed (direction not needed) at the moment considered. Source: a speedometer, a speed measurement, or computed from v = s/t. |
Choose the inputs correctly
Enter two of the three quantities. Kinetic energy requires mass and speed, mass requires energy and speed, speed requires energy and mass. Since v enters squared, solving for v requires a square root, which loses the sign of the velocity.
How to use the calculator
Select the target quantity and enter the two known values with units. Make sure speed is entered in m/s, since km/h without conversion gives a wrong result.
Worked example
Given m = 100 kg and v = 15.81 m/s (about 56.9 km/h), substitution gives Ek = 0.5 · 100 kg · 15.81² ≈ 12,500 J = 12.5 kJ.
Understand the result and units
A kinetic energy of 12.5 kJ is the work needed to accelerate the body from rest to this speed — and also the amount of energy that must be dissipated as heat, deformation or other forms if the body is brought to a complete stop.
The SI unit is the joule (J = kg·m²/s²). Larger amounts are given in kJ or MJ. Speed must be in m/s for SI calculations; 1 km/h equals 1/3.6 m/s.
Typical applications
Kinetic energy is used to estimate impact and crash energy, design braking systems, in materials handling, and for rotating flywheel masses (there using moment of inertia instead of mass).
Assumptions, limits and common mistakes
The formula applies to translational motion of a point mass or rigid body without rotation. Rotating components additionally have rotational energy (½·J·ω²), not included here. At relativistic speeds (near the speed of light), the classical formula no longer applies either.
Common mistake: Do not confuse the quadratic relationship with a linear one: double the speed means quadruple the energy, not double. Also, convert speed to m/s before substituting, since using km/h unconverted overstates energy by a factor of about 3.6² ≈ 13.
Frequently asked questions
Why does impact energy quadruple at double the speed?
Because speed enters the formula squared (v²). Doubling v therefore quadruples v² and thus Ek.
How are kinetic energy and stopping distance related?
At roughly constant braking force, stopping distance is proportional to kinetic energy and therefore also proportional to v². Doubling speed means roughly quadrupling stopping distance.
Should speed be entered in m/s or km/h?
For an SI-consistent result in joules, use m/s. Convert km/h by dividing by 3.6 first.