2,000
J
2
kJ
20
m/s
10
kg
200
kg·m/s
200
J/kg
2,000
J
2
kJ
20
m/s
10
kg
200
kg·m/s
200
J/kg
Kinetic energy is the energy an object possesses due to its motion. Any object with mass that is moving carries kinetic energy proportional to its mass and the square of its velocity. This concept is central to mechanics, vehicle safety engineering, ballistics, and sports science. The kinetic energy formula $$KE = \frac{1}{2}mv^2$$ shows that doubling velocity quadruples the energy, which is why highway collisions are far more destructive than low-speed ones.
This Kinetic Energy Calculator operates in three modes: compute KE from mass and velocity, find velocity from known KE and mass, or determine mass from known KE and velocity. The reverse calculations use the rearranged forms $$v = \sqrt{2 \cdot KE / m}$$ and $$m = 2 \cdot KE / v^2$$. These are indispensable in crash reconstruction, projectile analysis, and physics coursework. The calculator handles everything from subatomic particles to spacecraft, with results in both joules and kilojoules.
The fundamental kinetic energy equation is:
$$KE = \frac{1}{2}mv^2$$
where $$m$$ is mass in kilograms and $$v$$ is velocity in meters per second. The factor $$\frac{1}{2}$$ arises from integrating $$F = ma$$ over distance. To find velocity from kinetic energy, rearrange to $$v = \sqrt{\frac{2 \cdot KE}{m}}$$. To find mass, use $$m = \frac{2 \cdot KE}{v^2}$$. Note the quadratic dependence on velocity: a car traveling at 100 km/h has four times the kinetic energy of the same car at 50 km/h, which is why stopping distance scales with the square of speed.
Kinetic energy is always non-negative since mass and velocity squared are both positive. A 1 kg ball at 10 m/s has 50 J, roughly the energy of a small apple falling 5 meters. A 1,500 kg car at 30 m/s (108 km/h) carries 675,000 J — enough to significantly deform metal structures. In the reverse mode, a velocity result tells you how fast an object must move to carry a given energy.
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A 75 kg runner at 8 m/s has KE = ½ × 75 × 64 = 2400 J (2.4 kJ).
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A 50 g bullet with 500 J of KE travels at v = √(2×500/0.05) ≈ 141.4 m/s.
The $$v^2$$ dependence comes from integrating Newton's second law ($$F = ma$$) over displacement. Since $$a = dv/dt$$ and $$ds = v \, dt$$, the integral $$\int F \, ds = \int m \, v \, dv = \frac{1}{2}mv^2$$. This quadratic relationship means small increases in speed produce large increases in energy.
Kinetic energy is a scalar quantity. It has magnitude but no direction. This is because it depends on the square of velocity ($$v^2$$), which eliminates directional information. Two objects moving in opposite directions at the same speed have equal kinetic energy.
Kinetic energy is energy of motion ($$\frac{1}{2}mv^2$$), while potential energy is energy of position or configuration (e.g., $$mgh$$ for gravity). Together, they form mechanical energy. In a conservative system, one converts into the other while total mechanical energy is conserved.
No. The classical formula $$KE = \frac{1}{2}mv^2$$ is accurate only for speeds much less than the speed of light. At relativistic speeds, the correct formula is $$KE = (\gamma - 1)mc^2$$, where $$\gamma = 1/\sqrt{1 - v^2/c^2}$$.
Stopping distance is proportional to kinetic energy because the brakes must do work equal to the KE to bring the vehicle to rest. Since $$KE \propto v^2$$, doubling speed quadruples both kinetic energy and stopping distance (assuming constant braking force).
Earth (mass ≈ 5.97 × 10²⁴ kg) orbits the Sun at about 29,780 m/s. Its orbital kinetic energy is approximately $$KE = \frac{1}{2}(5.97 \times 10^{24})(29780)^2 \approx 2.65 \times 10^{33}$$ joules — an astronomically large value.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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