What is the formula for calculating work in physics?

Work is calculated using W = F × d × cos(θ), where F is the force in Newtons, d is the displacement in meters, and θ is the angle between force and displacement. When force and displacement are parallel, cos(0°) = 1, simplifying to W = F × d.

How do you calculate kinetic energy?

Kinetic energy is calculated using KE = ½mv², where m is mass in kilograms and v is velocity in meters per second. The result is in Joules (J).

What is the relationship between work and energy?

The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE = KE_final - KE_initial. This means work transfers energy to or from an object.

How do you calculate power from work?

Power is the rate of doing work: P = W/t, where W is work in Joules and t is time in seconds. Power can also be calculated as P = F × v (force times velocity). The SI unit is Watts (W).

Work Energy Calculator - Free Physics Calculator for Work, KE, PE, Power

Essential Work and Energy Equations

Master these fundamental physics formulas for energy calculations

W = F × d × cos(θ)

Work Done by Force

KE = ½mv²

Kinetic Energy

PE = mgh

Gravitational Potential Energy

PE = ½kx²

Elastic Potential Energy

P = W / t = F × v

Power

η = (Output/Input) × 100%

Efficiency

Energy Efficiency Calculator

Calculate the efficiency of machines and energy systems. Find out how much energy is lost.

Method 1: Energy Values

Energy Input (Joules)

Useful Energy Output (Joules)

Method 2: Power Values

Power Input (Watts)

Power Output (Watts)

Reset

Complete Guide to Work and Energy Calculations

Our free work energy calculator helps students, teachers, and engineers solve physics problems involving mechanical energy transformations. Whether you need a kinetic energy calculator, potential energy calculator, or power calculator physics tool, we provide accurate calculations with detailed step-by-step solutions.

What is Work in Physics?

Work is done when a force causes displacement. The formula W = F × d × cos(θ) calculates work in Joules. Work is positive when force and displacement are in the same direction, negative when opposite, and zero when perpendicular.

Understanding Kinetic Energy

Kinetic energy (KE = ½mv²) is the energy of motion. Double the velocity, and kinetic energy quadruples! This relationship is crucial for understanding vehicle safety and sports physics.

Potential Energy Types

Gravitational PE (mgh) depends on height, while elastic PE (½kx²) depends on spring compression. Both represent stored energy that can be converted to kinetic energy.

Power and Efficiency

Power measures how fast work is done (P = W/t). Efficiency tells us how much input energy becomes useful output. Real machines always have efficiency less than 100%.

The Work-Energy Theorem Explained

The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W = ΔKE = ½mv₂² - ½mv₁². This fundamental principle connects force, motion, and energy, making it essential for solving physics problems.

Conservation of Mechanical Energy

In the absence of non-conservative forces (like friction), mechanical energy is conserved: KE₁ + PE₁ = KE₂ + PE₂. This principle allows us to solve complex problems involving pendulums, roller coasters, and projectile motion without using force analysis.

Common Applications

Engineering: Calculate power requirements for machines and motors
Physics Education: Solve homework problems with step-by-step guidance
Sports Science: Analyze kinetic energy in athletics and vehicle dynamics
Renewable Energy: Calculate efficiency of solar panels and wind turbines
Construction: Determine work done by cranes and heavy machinery

How to Use This Calculator

Select the type of calculation you need (Work, Kinetic Energy, Potential Energy, Power, or Efficiency)
Enter your known values in the appropriate fields
Click the Calculate button to see instant results
Review the step-by-step solution to understand the process

Frequently Asked Questions

Q: What is the unit of work and energy?
A: The SI unit is the Joule (J). 1 Joule = 1 Newton × 1 meter = 1 kg⋅m²/s²

Q: Can work be negative?
A: Yes! Work is negative when force opposes motion, like friction slowing an object down.

Q: What's the difference between power and energy?
A: Energy is the capacity to do work (measured in Joules), while power is the rate of energy transfer (measured in Watts, where 1 W = 1 J/s).