How do I calculate kinetic energy?

Kinetic energy is KE = ½mv², where m is mass in kilograms and v is speed in meters per second. A 70 kg person running at 3 m/s has KE = 0.5 × 70 × 9 = 315 J. Doubling speed quadruples kinetic energy because it appears squared in the formula.

What is the difference between work and energy?

Energy is the capacity to do work; work is energy transferred by a force acting over a distance. Both are measured in joules. When you lift a 10 kg box 2 m, you do W = mgh = 10 × 9.81 × 2 = 196.2 J of work, which equals the potential energy gained by the box.

How do I convert joules to kilowatt-hours?

1 kWh = 3,600,000 J. So joules ÷ 3,600,000 = kWh. A 100 W light bulb running for 1 hour uses 360,000 J = 0.1 kWh. Residential electricity is billed per kWh — typically around $0.12–0.20 per kWh in the US.

What is a Calorie in physics vs nutrition?

In physics, 1 calorie (lowercase c) = 4.184 J — the energy to raise 1 g of water by 1°C. In nutrition, 1 Calorie (uppercase C, also called kilocalorie or kcal) = 4,184 J = 1,000 physics calories. This calculator uses the nutritional Calorie (kcal). A 500 J workout = about 0.12 kcal, which is why exercise burns surprisingly few food-Calories relative to daily intake.

What is conservation of energy?

The law of conservation of energy states that total mechanical energy (KE + PE) is constant in an isolated system with no non-conservative forces (like friction). A ball dropped from 10 m converts all PE to KE by the time it hits the ground: PE = mgh = m × 9.81 × 10; KE = ½mv² = same value. This gives v = √(2gh) = √(2 × 9.81 × 10) ≈ 14 m/s.

What is potential energy formula?

Gravitational potential energy is PE = mgh, where m is mass (kg), g is gravitational acceleration (9.81 m/s² on Earth), and h is height above a reference point (m). A 1 kg book on a 1 m shelf has PE = 1 × 9.81 × 1 = 9.81 J relative to the floor. PE depends on the chosen reference height — only changes in PE are physically meaningful.

How does the angle affect work done by a force?

Work = F × d × cos(θ), where θ is the angle between the force direction and displacement direction. At θ = 0° (force parallel to motion), cos(0) = 1 — maximum work. At θ = 90° (force perpendicular), cos(90) = 0 — no work done (like a person carrying a box horizontally while walking). At θ > 90°, work is negative — the force opposes motion.

What is the difference between horsepower and watts?

Both are units of power (energy per time). 1 horsepower (hp) = 745.7 watts. A 100 hp car engine = 74,570 W. Watts are the SI unit; horsepower comes from James Watt's comparison to draft horses. An average human sustains about 80–100 W (≈ 0.1 hp) of mechanical output during moderate exercise.

Energy & Work Calculator

KE = ½mv² · PE = mgh · W = F·d·cos θ · P = W/t — with unit converter & conservation of energy

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Mass (kg)

Velocity (m/s)

Results

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Joules (J)

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Kilojoules (kJ)

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kWh

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Calories (Cal)

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BTU

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Real-world

KE = ½mv²Kinetic Energy

PE = mghPotential

W = F·d·cos θWork

Energy Breakdown

Conservation of Mechanical Energy

In an ideal system (no friction), total energy KE + PE stays constant between any two states. Enter the initial and final conditions — the calculator solves for the missing value.

System Inputs

Mass (kg)

State 1 — Initial

Height h₁ (m)

Velocity v₁ (m/s)

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State 2 — Final

Height h₂ (m)

Velocity v₂ (m/s)

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Solved automatically

Energy Balance

KE (J)PE (J)Total (J)

State 1 — — —

State 2 — — —

Final velocity v₂ —

Energy Unit Converter

Enter any energy value and see it converted to all common units instantly.

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Common Conversions Reference

1 kWh = 3,600,000 J

One hour of 1,000 W consumption

1 Cal = 4,184 J

1 food Calorie (kcal)

1 BTU = 1,055 J

British Thermal Unit

1 hp·h = 2,685,000 J

One horsepower for one hour

Energy & Work Calculator

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Understanding Energy, Work, and Power in Physics

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Energy & Work Calculator

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Understanding Energy, Work, and Power in Physics

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