Kinetic Energy Calculator
Calculate kinetic energy from mass and velocity. Supports relativistic KE, rotational KE, momentum-to-KE, and elastic collision analysis.
kg
m/s
Kinetic Energy
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Kinetic Energy —
Equivalent Height (drop) —
Extended More scenarios, charts & detailed breakdown ▾
kg
m/s
Kinetic Energy (J)
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Kinetic Energy (kJ) —
Equivalent Height —
Professional Full parameters & maximum detail ▾
kg
m/s
Classical & Relativistic
Classical KE —
Relativistic KE —
Rotational & Units
Rotational KE (Iω²/2) —
KE in eV —
TNT Equivalent —
Dynamics
Stopping Distance —
How to Use This Calculator
- Enter mass in kilograms and velocity in m/s.
- See kinetic energy in joules and kilojoules, plus the equivalent drop height.
- Use From Momentum tab to compute KE from momentum and mass.
- Use Collision tab to compare KE before and after an elastic collision.
- The Professional tab adds relativistic KE, rotational KE, TNT equivalent, and stopping distance.
Formula
Classical KE = ½mv²
Equivalent height: h = v²/(2g)
From momentum: KE = p²/(2m)
Relativistic: KE = (γ−1)mc² | γ = 1/√(1−v²/c²)
Example
A 2 kg ball moving at 10 m/s: KE = ½ × 2 × 10² = 100 J. Equivalent height = 100/(2×9.81) = 5.1 m.
Frequently Asked Questions
- Kinetic energy (KE) is the energy an object possesses due to its motion. The classical formula is KE = ½mv², where m is the object's mass in kilograms and v is its speed in meters per second. The result is in joules (J). For example, a 2 kg ball moving at 10 m/s has KE = ½ × 2 × 10² = 100 J. Kinetic energy is a scalar quantity (has magnitude but no direction). It is always positive (or zero for a stationary object). When an object decelerates and stops, its kinetic energy converts to heat, sound, or deformation energy.
- Kinetic energy is proportional to velocity squared (v²), so doubling velocity increases kinetic energy by a factor of 4 (2² = 4). Tripling velocity increases KE by 9×. This quadratic relationship is why car crash severity increases so dramatically with speed: a car at 60 mph has 4× more kinetic energy than the same car at 30 mph. By contrast, doubling the mass only doubles the kinetic energy (linear relationship). This is why vehicle speed is much more critical than vehicle weight in collision energy calculations — controlling speed is more effective for safety.
- At speeds approaching the speed of light (c ≈ 3 × 10⁸ m/s), the classical formula ½mv² underestimates the true kinetic energy. The relativistic formula is KE = (γ − 1)mc², where γ = 1 ÷ √(1 − v²/c²) is the Lorentz factor and c is the speed of light. At 10% of c, the relativistic KE is about 0.5% higher than classical. At 50% of c, it is 15% higher. At 90% of c, it is 130% higher. As v → c, γ → ∞ and KE → ∞, which is why no massive object can reach the speed of light — it would require infinite energy.
- Momentum p = mv (mass × velocity, units: kg·m/s). Kinetic energy in terms of momentum: KE = p² ÷ (2m). This is useful when momentum is known rather than velocity directly. For example, a 5 kg object with momentum 20 kg·m/s: KE = 20² ÷ (2 × 5) = 400 ÷ 10 = 40 J. Alternatively, p = √(2m × KE). In collisions, momentum is conserved in all collision types, while kinetic energy is conserved only in perfectly elastic collisions. The From Momentum tab in this calculator accepts mass and momentum to compute KE.
- An object at height h above the ground has gravitational potential energy PE = mgh. If it falls from rest to ground level, all PE converts to KE: mgh = ½mv² → h = v² ÷ (2g). This gives the "equivalent drop height" — the height from which an object would need to free-fall to reach speed v. For example, a car at 60 km/h (16.67 m/s) has equivalent height = 16.67² ÷ (2 × 9.81) = 277.9 ÷ 19.62 = 14.2 m. Equivalently, h = KE ÷ (mg). This concept is used in vehicle safety testing and free-fall analysis.