Kinetic Energy

Online calculator and formulas for calculating kinetic energy

Kinetic Energy Calculator

Calculate energy of motion

Calculates the kinetic energy from mass and velocity. The kinetic energy depends quadratically on velocity.

J
kg
m/s
Result
Energy:
Mass:
Velocity:

Example Calculation

Example: Moving Car
Problem:

A car with a mass of 1500 kg is traveling at a speed of 60 km/h (16.67 m/s). What kinetic energy does the car have?

Given:
  • Mass m = 1500 kg
  • Velocity v = 60 km/h = 16.67 m/s
  • Find: Kinetic energy E
Solution:
\[E = \frac{1}{2} \times m \times v^2\]
\[E = \frac{1}{2} \times 1500 \text{ kg} \times (16{.}67 \text{ m/s})^2\]
\[E = \frac{1}{2} \times 1500 \times 277{.}9 = 208{,}425 \text{ J} ≈ 208{.}4 \text{ kJ}\]
Practical Applications
Traffic safety: Braking distance, impact energy, crash tests
Mechanical engineering: Flywheels, energy storage, turbines
Sports science: Throwing distance, jumping power, performance analysis
Velocity Dependence
Quadratic relationship:
  • 30 km/h: E₁
  • 60 km/h: 4 × E₁
  • 90 km/h: 9 × E₁
  • 120 km/h: 16 × E₁
  • 150 km/h: 25 × E₁
  • 180 km/h: 36 × E₁

Formulas for kinetic energy

The kinetic energy or energy of motion is the energy that an object contains due to its motion. It depends on the mass and velocity of the moving body and increases quadratically with velocity.

Calculate kinetic energy

Basic formula for kinetic energy from mass and velocity.

\[\displaystyle E = \frac{1}{2} \times m \times v^2\]
E = Energy [J], m = Mass [kg], v = Velocity [m/s]
Calculate mass

Rearrangement to calculate mass from known energy.

\[\displaystyle m = \frac{2 \times E}{v^2}\]
Mass from energy and velocity
Calculate velocity

Rearrangement to calculate velocity from known energy.

\[\displaystyle v = \sqrt{\frac{2 \times E}{m}}\]
Velocity from energy and mass
Important Notes
  • Kinetic energy increases quadratically with velocity
  • Double velocity means four times the kinetic energy
  • Important for traffic safety: braking distance increases quadratically with velocity
  • SI unit: Joule (J) = kg × m²/s²

Detailed description of kinetic energy

Definition and Significance

The kinetic energy or energy of motion is the energy that an object contains due to its motion. It corresponds to the work that must be applied to set the object in its current motion.

Usage Instructions

To calculate, select the value to be calculated using the radio buttons. Then enter the corresponding value and click the 'Calculate' button.

Application Areas

Traffic Safety

Braking distance, impact energy, crash test analyses. Safety assessment at different velocities.

Mechanical Engineering

Flywheels, energy storage, turbines, rotating machinery. Dimensioning of braking systems and clutches.

Sports Science

Throwing distance, jumping power, performance analysis. Optimization of movement sequences and training methods.

Understanding Kinetic Energy

Kinetic energy depends on mass and velocity, with velocity having a quadratic influence:

Low Velocity

Pedestrian (5 km/h):
70 kg × (1.4 m/s)² = 68 J
Bicycle (20 km/h):
80 kg × (5.6 m/s)² = 1254 J

Medium Velocity

Car in city (50 km/h):
1500 kg × (13.9 m/s)² = 145 kJ
Car on highway (100 km/h):
1500 kg × (27.8 m/s)² = 579 kJ

High Velocity

Car on highway (150 km/h):
1500 kg × (41.7 m/s)² = 1.3 MJ
High-speed train:
400 t × (83.3 m/s)² = 1.39 GJ

Insight: At double velocity, four times more energy is needed to brake - hence the dramatic increase in accident severity at higher velocities!


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