Kinetic Energy Calculator — Translational & Rotational KE

Calculate kinetic energy (½mv²) or rotational KE (½Iω²). Supports kg/lb, m/s/mph/km/h, and RPM conversion. Joules or foot-pounds output.

July 14, 2026

Calculation Mode

Energy Output Unit

Mass

Velocity

Kinetic Energy

300,000 J

1,500 kg at 20 m/s

The v² Relationship

At double the speed (40 m/s), the same mass would carry 1,200 kJ — exactly 4× the energy, because velocity is squared in the formula.

Translational KE = ½ × mass × velocity². Rotational KE = ½ × moment of inertia × angular velocity², with RPM converted to rad/s via ω = RPM × 2π ÷ 60. Mass converts from pounds using 1 lb = 0.453592 kg; velocity converts from mph (1 mph = 0.44704 m/s) or km/h (1 km/h = 0.277778 m/s); energy converts to foot-pounds using 1 J = 0.737562 ft-lb.

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Reference Values

Last verified: Jul 11, 2026

Category	Range	What It Means	Status
Translational kinetic energy ★	KE = ½ × m × v²	Mass (kg) times velocity squared (m/s), times one-half. Result is in joules (J). This is the energy of an object moving in a straight line.	★ Best
Rotational kinetic energy ★	KE = ½ × I × ω²	Moment of inertia (kg·m²) times angular velocity squared (rad/s), times one-half. A distinct formula for spinning objects — I must be entered directly since deriving it from an object's shape and mass distribution is beyond this calculator's scope.	★ Best
Angular velocity from RPM	ω = RPM × 2π ÷ 60	Converts revolutions per minute to radians per second, the unit the rotational KE formula requires.	Good
The v² relationship ★	2× speed = 4× KE	Because velocity is squared, doubling speed quadruples kinetic energy — tripling speed makes it 9× larger. This is why small increases in speed matter so much for stopping distance and crash severity.	★ Best
Mass: pounds to kilograms	1 lb = 0.453592 kg	Standard avoirdupois pound conversion, used to convert mass entries into kilograms before the formula runs.	Good
Velocity: mph to m/s	1 mph = 0.44704 m/s	Exact conversion (1 mile = 1,609.344 m, 1 hour = 3,600 s).	Good
Velocity: km/h to m/s	1 km/h = 0.277778 m/s	Exact conversion (1 km = 1,000 m, 1 hour = 3,600 s).	Good
Energy: joules to foot-pounds	1 J = 0.737562 ft-lb	Used to display kinetic energy in the US customary foot-pound unit alongside the SI joule.	Good

Source: Standard classical mechanics formulas (Halliday/Resnick/Walker, Fundamentals of Physics) for translational and rotational kinetic energy; rotational KE distinction confirmed against Physics LibreTexts "9.5 Rotational Kinetic Energy." Unit conversion factors from NIST Special Publication 811 (Guide for the Use of the International System of Units).

Worked Examples

Sedan at City-Street Speed (Translational)

Mass: 1,500 kg
Velocity: 20 m/s (≈45 mph)

300,000 J (300 kJ)

KE = 0.5 × 1,500 × 20² = 0.5 × 1,500 × 400 = 300,000 J. In foot-pounds: 300,000 × 0.737562 ≈ 221,269 ft-lb.

90 mph Fastball (Translational, Unit Conversion)

Mass: 0.145 kg (regulation baseball)
Velocity: 90 mph

≈117.36 J

90 mph converts to 90 × 0.44704 = 40.2336 m/s. KE = 0.5 × 0.145 × 40.2336² = 0.5 × 0.145 × 1,618.74 ≈ 117.36 J (about 86.56 ft-lb).

Doubling Speed Quadruples Energy (Translational)

Mass: 1,000 kg (both runs)
Velocity: 15 m/s, then 30 m/s

112,500 J → 450,000 J (4×)

At 15 m/s: 0.5 × 1,000 × 225 = 112,500 J. At double the speed, 30 m/s: 0.5 × 1,000 × 900 = 450,000 J — exactly 4× the energy, because velocity is squared, not doubled linearly.

Flywheel at 1,800 RPM (Rotational)

Moment of Inertia (I): 2.5 kg·m²
Angular Velocity: 1,800 RPM

≈44,413 J (44.41 kJ)

1,800 RPM converts to ω = 1,800 × 2π ÷ 60 ≈ 188.50 rad/s. KE = 0.5 × 2.5 × 188.50² ≈ 1.25 × 35,530.6 ≈ 44,413 J.

Spinning Bicycle Wheel (Rotational, Direct rad/s)

Moment of Inertia (I): 0.15 kg·m²
Angular Velocity: 20 rad/s

30 J

KE = 0.5 × 0.15 × 20² = 0.5 × 0.15 × 400 = 30 J. Entered directly in rad/s, so no RPM conversion step is needed.

How to Use This Calculator

1

Choose a mode

Translational for straight-line motion (½mv²), or Rotational for spinning objects (½Iω²).
2

Enter your values

Translational mode needs mass and velocity. Rotational mode needs moment of inertia (I, in kg·m²) and angular velocity.
3

Pick your units

Mass in kg or lb, velocity in m/s, mph, or km/h, angular velocity in RPM or rad/s, and energy output in joules or foot-pounds.
4

Read the result

Updates instantly. Translational mode also shows how much energy the same mass would carry at double the speed, to illustrate the v² relationship.

What Each Value Means

Kinetic Energy (KE) (joules (J) or foot-pounds (ft-lb)): The energy an object has because it's moving, whether in a straight line (translational) or spinning (rotational). Measured in joules (J), or convertible to foot-pounds (ft-lb) for US customary work.
Moment of Inertia (I) (kg·m²): A rotating object's resistance to changes in spin rate — the rotational analog of mass. Depends on both the object's mass and how that mass is distributed relative to the axis of rotation.
Angular Velocity (ω) (rad/s (or RPM)): How fast an object is spinning, measured in radians per second. This calculator also accepts revolutions per minute (RPM) and converts it automatically using ω = RPM × 2π ÷ 60.

Frequently Asked Questions

What is the formula for kinetic energy?

Translational kinetic energy — the energy of an object moving in a straight line — is KE = ½ × m × v², where m is mass in kilograms and v is velocity in meters per second. The result comes out in joules (J), the SI unit of energy. This calculator also converts mass from pounds and velocity from mph or km/h automatically, so you can enter values in whatever unit you have on hand.

Why is velocity squared in the kinetic energy formula?

The v² term comes directly from the physics derivation of kinetic energy (integrating force over distance using Newton's second law), and it has a real-world consequence worth internalizing: doubling an object's speed doesn't double its kinetic energy — it quadruples it. Tripling the speed makes it 9× larger. This is why a car crash at 60 mph is far more than "twice as bad" as one at 30 mph, and why small increases in speed matter so much for stopping distance, crash severity, and braking energy.

What's the difference between translational and rotational kinetic energy?

Translational kinetic energy describes an object moving from one place to another in a straight line, using mass and linear velocity (KE = ½mv²). Rotational kinetic energy describes an object spinning around an axis — a flywheel, a wheel, a turbine rotor — and uses moment of inertia (I) and angular velocity (ω) instead: KE = ½Iω². The two formulas are structurally identical (mass ↔ inertia, velocity ↔ angular velocity) but describe different kinds of motion, and an object like a rolling wheel technically has both kinds of kinetic energy at once.

How do I convert RPM to rad/s for the rotational formula?

Multiply revolutions per minute by 2π and divide by 60: ω = RPM × 2π ÷ 60. One full revolution is 2π radians, and there are 60 seconds in a minute, so this conversion turns "revolutions per minute" into "radians per second," the unit the rotational kinetic energy formula requires. This calculator does the conversion for you when you select RPM as your angular velocity unit.

What is moment of inertia, and why can't this calculator derive it automatically?

Moment of inertia (I) measures how resistant an object is to changes in its rotational speed, and unlike mass, it depends on how that mass is distributed relative to the axis of rotation — a solid disk, a hollow ring, and a rod all have different I formulas even at the same mass and radius. Because deriving I correctly requires knowing the object's exact shape and mass distribution, this calculator asks you to enter I directly in kg·m², which you'd typically get from a shape-specific formula, an engineering reference, or a CAD tool.