KE Calculator - Kinetic Energy Calculator & KE = ½mv² Calculator
Free KE calculator & kinetic energy calculator. Calculate kinetic energy using the formula KE = ½mv². Supports multiple units for mass (kg, g, lb, oz) and velocity (m/s, km/h, mph, ft/s) with step-by-step physics solutions.
Last updated: October 30, 2025
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Kinetic Energy Result
Mass
2 kg
Velocity
10 ms
Energy Conversions:
Kilojoules:
0.10 kJ
Calories:
23.90 cal
Electron Volts:
6.24e+20 eV
The kinetic energy of an object with mass 2 kg moving at 10 ms is 100.00 joules. Kinetic energy represents the energy an object possesses due to its motion.
Step-by-Step Solution
- Step 1: Convert units to SI base units (kg and m/s)
- Mass: 2 kg (already in SI units)
- Velocity: 10 m/s (already in SI units)
- Step 2: Apply the kinetic energy formula
- KE = ½ × m × v²
- KE = ½ × 2.00 kg × (10.00 m/s)²
- KE = 0.5 × 2.00 × 100.00
- KE = 100.00 J
- Step 3: Final answer
- Kinetic Energy = 100.00 joules
Kinetic Energy Calculator Features
Formula
KE = ½ × m × v²
Standard kinetic energy equation
Supported Units
kg, g, lb, oz, m/s, km/h, mph, ft/s
Automatic SI unit conversion
Energy Units
J, kJ, cal, eV
Multiple energy unit outputs
Includes
Unit conversions & formula steps
Learn the KE calculation process
Key Insight
Double speed = 4× energy
Quadratic velocity dependence
Applications
Motion, collisions, energy
Essential physics calculations
Quick Example Result
Mass: 2 kg, Velocity: 10 m/s
Kinetic Energy
100 J
Formula
KE = ½ × 2 × 10²
How the KE Calculator Works
Our KE calculator uses the fundamental kinetic energy formula KE = ½mv² to calculate the energy of motion. The calculator automatically converts all inputs to SI base units (kilograms and meters per second), applies the formula, and provides results in joules along with conversions to other energy units. This follows standard physics principles from classical mechanics.
Kinetic Energy Formula
KE = ½ × m × v²Where:
- KE = Kinetic Energy (joules, J)
- m = Mass (kilograms, kg)
- v = Velocity (meters per second, m/s)
- ½ = Constant factor (from integration of work-energy theorem)
The factor of ½ comes from integrating force over distance when deriving the work-energy theorem. This formula is valid for point masses and objects moving at non-relativistic speeds.
Mathematical Foundation
Kinetic energy is derived from the work-energy theorem, which states that the work done on an object equals its change in kinetic energy. Starting from Newton's second law and integrating force over distance, we arrive at KE = ½mv². This formula is fundamental in classical mechanics and applies to all objects with mass moving at speeds much less than the speed of light.
- Kinetic energy is a scalar quantity (has magnitude but no direction)
- KE depends on velocity squared: doubling speed quadruples energy
- Kinetic energy is always positive or zero (never negative)
- At rest, objects have zero kinetic energy
- KE is frame-dependent: different observers measure different KE
- For relativistic speeds, use KE = (γ - 1)mc² where γ = 1/√(1 - v²/c²)
Applications of Kinetic Energy
Kinetic energy calculations are essential in many fields:
- Vehicle Safety: Crash analysis, airbag deployment, impact forces
- Sports Physics: Analyzing motion of balls, athletes, and projectiles
- Renewable Energy: Wind turbines converting kinetic energy to electrical energy
- Transportation: Fuel efficiency, braking distances, speed limits
- Collision Analysis: Elastic and inelastic collisions, momentum conservation
- Engineering: Machine design, energy efficiency, motion control systems
Sources & References
- University Physics - Young & Freedman (15th Edition)Comprehensive coverage of kinetic energy and work-energy theorem
- Fundamentals of Physics - Halliday, Resnick, Walker (11th Edition)Classic textbook on mechanics and energy concepts
- Khan Academy - Work and EnergyInteractive lessons on kinetic energy and energy conservation
Need help with other physics calculations? Try our momentum calculator or joules calculator.
Get Custom Calculator for Your PlatformKE Calculator Examples
Given:
- Mass: m = 2 kg
- Velocity: v = 10 m/s
- Formula: KE = ½mv²
Step-by-Step Solution:
- Convert to SI units (already in SI: kg and m/s)
- Apply formula: KE = ½ × m × v²
- KE = ½ × 2 kg × (10 m/s)²
- KE = 0.5 × 2 × 100
- KE = 100 J
Result: KE = 100 joules
The object has 100 J of kinetic energy due to its motion.
Example: Double Velocity
If velocity doubles to 20 m/s:
KE = ½ × 2 × 20² = 400 J (4× increase)
Example: Unit Conversion
Mass: 1000 g = 1 kg
Velocity: 36 km/h = 10 m/s
Frequently Asked Questions
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