Kinetic Energy (KE)
The energy an object possesses due to its motion. It depends on the mass ($m$) and velocity ($v$).
KE = ½ · m · v²
Work Energy Calculator
Calculate mechanical work, kinetic energy, or gravitational potential energy.
Work-Energy Calc
Calculate Kinetic, Potential, and Work-Energy transformations.
Energy Concepts
Energy exists in many forms. This calculator focuses on mechanical energy: the energy associated with the motion (Kinetic) and position (Potential) of an object.
Potential Energy (PE)
Gravitational potential energy is stored energy based on an object's height ($h$) and mass ($m$) in a gravity field ($g$).
PE = m · g · h
Work-Energy Theorem
The net work ($W$) done on an object equals its change in kinetic energy ($\Delta KE$).
W = KEfinal - KEinitial
work energy formulas and interpretation
Work transfers energy when force acts through displacement.
The calculator preserves work, kinetic-energy, and potential-energy modes.
How to use the work energy calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Work equals force times displacement times the cosine of their included angle.
W = Fd cos(θ)- W — Work
- Energy transferred (J)
- F — Force
- Applied force (N)
- d — Displacement
- Distance moved (m)
- θ — Angle
- Force-displacement angle (degrees)
Applied force example
A 20 N force moves an object 5 m in the same direction.
- Force
- 20 N
- Distance
- 5 m
- W = 20 × 5 × cos(0°)
- W = 100 J
Result: Work is 100 J.
The force transfers 100 joules.
Understanding your results
Interpreting the result
Positive work adds kinetic energy; negative work removes it.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.
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