What is the formula for kinetic energy?+
The formula for kinetic energy is KE = 0.5 × m × v², where KE is kinetic energy in joules (J), m is mass in kilograms (kg), and v is velocity in metres per second (m/s). This formula was derived from the work-energy theorem: the work done accelerating an object from rest equals the kinetic energy gained. It applies to any object with mass moving at speeds well below the speed of light.
What are the units of kinetic energy?+
The SI unit of kinetic energy is the joule (J), which equals 1 kg·m²/s². Other common units include kilojoules (kJ = 1,000 J), kilocalories (kcal = 4,184 J), kilowatt-hours (kWh = 3,600,000 J), British Thermal Units (BTU = 1,055 J), and foot-pound-force (ft·lbf = 1.356 J). This calculator converts to all six units simultaneously.
How does kinetic energy change with speed?+
Kinetic energy is proportional to the square of velocity. Doubling speed quadruples kinetic energy; tripling speed multiplies it by nine. This non-linear relationship explains why vehicle collision damage increases so dramatically with speed: a crash at 100 km/h releases four times the energy of a crash at 50 km/h. Speed is the dominant factor in both kinetic energy and stopping distance.
What is the difference between kinetic energy and potential energy?+
Kinetic energy (KE = 0.5mv²) is the energy of motion. Potential energy is stored energy due to position or configuration (for gravity: PE = mgh). An object falling from height h converts PE to KE. At the bottom of the fall, if all PE converts to KE, then 0.5mv² = mgh, so v = √(2gh). The total mechanical energy (KE + PE) is conserved in the absence of friction and air resistance.
What is the kinetic energy of a car at 100 km/h?+
100 km/h = 27.78 m/s. For a 1,500 kg car: KE = 0.5 × 1,500 × 27.78² = 578,600 J = 578.6 kJ = 138.3 kcal. This energy must be converted to heat by the brakes during a full stop. At 200 km/h, KE = 2,314,400 J, which is four times as much, explaining why stopping at high speed requires much greater braking force and distance.
What is momentum and how is it related to kinetic energy?+
Momentum (p) = mass × velocity = mv. Kinetic energy can also be expressed as KE = p² / (2m). While both depend on mass and velocity, momentum is linear in v while kinetic energy is quadratic. In collisions, momentum is always conserved, but kinetic energy is only conserved in elastic collisions. In real-world inelastic collisions, kinetic energy converts to heat and deformation.
How do I find velocity from kinetic energy and mass?+
Rearrange KE = 0.5mv² to get v = √(2 × KE / m). For example, an object with KE = 100 J and mass = 2 kg has v = √(2 × 100 / 2) = √100 = 10 m/s. Use the Find Velocity tab in this calculator, enter the kinetic energy and mass, and click Calculate to get the result instantly along with all unit conversions.
What is the kinetic energy of a bullet?+
A typical 9 mm handgun bullet weighs about 8 g (0.008 kg) and travels at 370 m/s. KE = 0.5 × 0.008 × 370² = 547.9 J. A rifle bullet (5.56 NATO) weighs about 4 g (0.004 kg) at 945 m/s: KE = 0.5 × 0.004 × 945² = 1,788 J. The high velocity is the dominant factor because energy scales as v².
Does kinetic energy depend on direction?+
No. Kinetic energy is a scalar quantity with magnitude only and no direction. It depends on speed (the magnitude of velocity), not the direction of motion. An object moving east at 10 m/s has the same kinetic energy as one moving west or north at 10 m/s with the same mass. In contrast, momentum is a vector and does depend on direction.
What is the relativistic kinetic energy formula?+
At speeds approaching the speed of light, the Newtonian formula KE = 0.5mv² becomes inaccurate. The relativistic formula is KE = (γ - 1)mc², where γ = 1/√(1 - v²/c²) is the Lorentz factor and c = 299,792,458 m/s. At everyday speeds (below about 10% of c), the difference is less than 0.5%, so the classical formula is accurate for all practical purposes.
How much kinetic energy does a running person have?+
A 70 kg person running at 4 m/s (about 14.4 km/h): KE = 0.5 × 70 × 16 = 560 J. At a sprint of 10 m/s: KE = 0.5 × 70 × 100 = 3,500 J = 3.5 kJ. Usain Bolt's world record speed was about 10.44 m/s. The energy differences between walking and running are substantial, which is why energy expenditure increases sharply with running pace.
What is the equivalent fall height for a given kinetic energy?+
An object with kinetic energy KE could have gained that energy by falling from a height h = KE / (mg). For example, a 1 kg object with KE = 500 J has an equivalent height of 500 / (1 × 9.81) = 51 m. This is the height from which the object would need to fall from rest, ignoring air resistance, to reach that kinetic energy at the bottom. This calculator shows this value for every calculation.