How do I convert joules to kilowatt-hours?

1 kWh = 3,600,000 J (3.6 MJ). To convert joules to kWh, divide by 3,600,000. For example, 7,200,000 J = 2 kWh. This conversion is useful when comparing mechanical energy to electrical energy consumption.

Is kinetic energy a vector or scalar?

Kinetic energy is a scalar quantity — it has magnitude but no direction. Even though velocity is a vector, squaring it removes the directional information. Two objects moving in opposite directions at the same speed have the same kinetic energy.

Kinetic Energy Calculator

Calculate kinetic energy using KE = ½mv². Solve for KE, mass, or velocity with full unit conversion, relativistic mode, and rotational KE.

Solve for:

Presets:

Mass (m)

Velocity (v)

Kinetic Energy (KE)

Fill in two known values — the third is calculated automatically.

Relativistic Mode

KE = (γ−1)mc², γ = 1/√(1−v²/c²)

Mass (m) kg

Velocity (v) m/s

Rotational Kinetic Energy

KE_rot = ½·I·ω²

Moment of Inertia (I) kg·m²

Angular Velocity (ω) rad/s

What Is Kinetic Energy?

Kinetic energy is the energy that an object possesses by virtue of its motion. Any moving object — from an electron to a galaxy — carries kinetic energy proportional to its mass and the square of its speed. It is measured in joules (J) in the SI system.

The word "kinetic" derives from the Greek kinetikos (moving). The concept was developed through the 17th–19th centuries by Leibniz, du Châtelet, and others. Émilie du Châtelet's experimental work in the 1740s confirmed that KE is proportional to v² (not v, as Newton assumed), which revolutionized mechanics.

½mv²

Classical kinetic energy formula

v²

Double velocity → 4× the energy

Scalar

No direction — only magnitude in joules

The KE Formula Explained

Solve for KE

KE = ½mv²

Given mass and velocity.

Solve for Mass

m = 2KE / v²

Given KE and velocity.

Solve for Velocity

v = √(2KE/m)

Given KE and mass.

Example 1 — Car at 100 km/h

m = 1500 kg, v = 27.78 m/s

KE = ½ × 1500 × 27.78²

KE ≈ 578,703 J ≈ 579 kJ

Example 2 — Bullet

m = 0.008 kg, v = 400 m/s

KE = ½ × 0.008 × 400²

KE = 640 J

Example 3 — Find velocity from KE

KE = 1000 J, m = 50 kg

v = √(2 × 1000 / 50)

v = √40 ≈ 6.32 m/s

Example 4 — ISS in orbit

m = 419,725 kg, v = 7,660 m/s

KE = ½ × 419725 × 7660²

KE ≈ 1.232 × 10¹³ J

Translational vs Rotational KE

A moving object can have translational KE (moving through space) and/or rotational KE (spinning). A rolling ball has both simultaneously.

Type	Formula	Variables	Example
Translational	½mv²	m = mass, v = linear speed	Car moving at 60 mph
Rotational	½Iω²	I = moment of inertia, ω = angular speed	Spinning flywheel
Total (rolling)	½mv² + ½Iω²	Both contributions	Rolling bowling ball

Energy Comparison Table

Approximate kinetic energies of everyday objects to put your calculations in context.

Object	Mass	Speed	KE (J)
Walking person	70 kg	1.4 m/s	68.6 J
Cricket ball (delivery)	0.16 kg	40 m/s	128 J
Rifle bullet	0.008 kg	400 m/s	640 J
Car at 100 km/h	1,500 kg	27.8 m/s	578,704 J
Boeing 747 (cruise)	280,000 kg	250 m/s	8.75 × 10⁹ J
ISS in orbit	419,725 kg	7,660 m/s	1.23 × 10¹³ J

Relativistic Kinetic Energy

At speeds approaching the speed of light (c = 299,792,458 m/s), classical mechanics breaks down. Einstein's special relativity gives a corrected formula:

KE = (γ − 1) · m · c²

where γ = 1 / √(1 − v²/c²)

The Lorentz factor γ approaches infinity as v approaches c, meaning it takes infinite energy to accelerate a massive object to the speed of light. For v < 0.1c, the classical and relativistic formulas agree to within 0.5%.

Frequently Asked Questions

Kinetic energy is the energy an object possesses due to its motion. Any object with mass that is moving has kinetic energy, calculated as KE = ½mv² where m is mass in kilograms and v is velocity in m/s. The result is in joules (J).

Velocity is squared in KE = ½mv², while mass appears only once. This means doubling the velocity quadruples the kinetic energy, but doubling the mass only doubles it. A bullet travelling at 400 m/s has far more KE than a heavy object moving slowly.

1 kWh = 3,600,000 J (3.6 MJ). To convert joules to kWh, divide by 3,600,000. For example, 7,200,000 J = 2 kWh. This is useful when comparing mechanical energy to electrical energy consumption.

Kinetic energy is a scalar quantity — it has magnitude but no direction. Even though velocity is a vector, squaring it removes directional information. Two objects moving in opposite directions at the same speed have identical kinetic energies.

Rotational kinetic energy is the energy of a spinning object: KE_rot = ½Iω², where I is the moment of inertia (kg·m²) and ω is the angular velocity (rad/s). It is the rotational analogue of linear kinetic energy ½mv².

The classical KE = ½mv² formula is accurate for speeds below about 10% of the speed of light (~30,000 km/s). For particles in accelerators, cosmic rays, or any object approaching c = 299,792,458 m/s, use the relativistic formula KE = (γ−1)mc².

The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = KE_final − KE_initial. This means kinetic energy and work are measured in the same unit (joules) and are directly interchangeable.

Use SI units for direct results: mass in kg, velocity in m/s. The result will be in joules (J). Our calculator handles conversions automatically — you can input in lb, mph, km/h, etc. and get results in J, kJ, cal, kcal, kWh, or ft·lb.

Related Calculators

Gravitational Potential Energy Newton's Second Law Projectile Motion Free Fall Calculator Ohm's Law Calculator