A 2 kg object at 3 m/s
E = ½ × m × v²
Square the speed first: 3² = 9. Then multiply by half the mass: ½ × 2 × 9 = 9 J. At 6 m/s, the same mass would have 36 J.
Energy of motion
Kinetic Energy Calculator
Find the energy of a moving object, or solve for its speed or mass. Enter two known quantities and choose convenient units.
Calculate kinetic energy, speed, or mass
Kinetic energy
Enter two known quantities, then select Calculate.
- Kinetic energy (SI)
- Mass (SI)
- Speed (SI)
- Formula
≈ marks display rounding. This is a classical translational model for speeds much lower than light speed. Calculations run in your browser. Press Enter to calculate. Successful results appear in this tab's Recent calculations.
Three worked examples
25 J with a mass of 2 kg
v = √(2E ÷ m)
Twice the energy divided by mass is 50 ÷ 2 = 25. Its nonnegative square root gives 5 m/s, equivalent to 18 km/h.
36 J at 12 km/h
m = 2E ÷ v²
Convert 12 km/h to 10/3 m/s without rounding. Dividing 72 by 100/9 gives 6.48 kg. Keeping the speed unrounded avoids an unnecessary conversion error.
Formula, units, and scope
The classical translational relationship is E = ½mv². It gives energy in joules when mass is in kilograms and speed is in meters per second. This calculator uses speed as a nonnegative magnitude, not a signed component of velocity. It excludes rotational, vibrational, and relativistic energy.
Inputs and conversions use exact fractions. The international avoirdupois pound is 0.45359237 kg; 1 ft/s is 0.3048 m/s; 1 mph is 0.44704 m/s; and 1 km/h is exactly 5/18 m/s. A kilojoule is 1,000 J and a megajoule is 1,000,000 J. Here lb denotes mass, not pound-force.
Square roots are retained exactly until the final display, including irrational roots. Display rounding uses exact midpoint comparisons, with halfway values rounded away from zero. Trailing zeros are removed. Decimal places control the display and do not represent measurement accuracy or significant figures. If a positive quantity rounds to zero, a notice distinguishes it from an actual zero.
The formula is suitable for speeds much lower than light speed. A result at or above 10% of vacuum light speed triggers a reminder to use a relativistic model; this is a display reminder threshold, not a universal accuracy guarantee below it. Inputs implying speeds at or above light speed receive a stronger notice. The tool still evaluates the classical expression, so a numeric answer does not establish physical validity.
Each input accepts up to 15 integer digits and 10 decimal digits within 64 characters. References: OpenStax: Kinetic Energy for the classical relationship and reference frames; NIST conversion factors and NIST footnote 22 for the exact pound definition. See our calculation policy for shared rules.
Common questions
Can speed or kinetic energy be zero?
Yes. For a positive mass, zero speed gives zero kinetic energy, and zero kinetic energy gives zero speed. When finding mass, this tool requires positive energy and speed. If both are zero, any positive mass fits the equation; if only one is zero, no positive mass fits.
Why does the calculator reject a negative speed?
Speed measures magnitude and is nonnegative. A negative velocity component describes a direction. Use the object's speed in your chosen reference frame; if its velocity is −3 m/s along one axis, its speed is 3 m/s.
Is kinetic energy the same as force?
No. Energy is measured in joules and force in newtons. Energy alone does not determine an impact force; the interaction also depends on how the object slows down, including distance or time and the force profile.
Does this include a spinning object's energy?
No. It accounts for translational motion. A spinning wheel can also have rotational kinetic energy, which requires its moment of inertia and angular speed. Do not interpret this result as the total energy of every moving system.
Why can a result display ≈ 0?
A positive value may be smaller than the selected display precision. Increase the decimal places or choose a smaller result unit where available. The unrounded fraction or square root is kept internally.