VECTOR LAB
Your first experiment

Choose a formula. Change a value. Inspect what moves.

The result, worked steps, and live model stay connected. Start with any subject—the calculations stay on this device.

Kinetic Energy Calculator

Kinetic energy is ½mv². This tool first evaluates velocity at time t using v = v₀ + at, then calculates the energy at that instant. Set acceleration to zero to use a fixed velocity.

Worked example: With mass 2 kg, initial velocity 3 m/s, acceleration 0 m/s², and any elapsed time, Eₖ = ½ × 2 × 3² = 9 J.

Assumptions and units: Use kilograms, meters per second, and seconds. Velocity may be negative because it includes direction, but energy is nonnegative. The classical formula is unsuitable near the speed of light.

Read the full lesson and self-check

calculated in real time

Select a formula, tune the variables, and see the model respond. No black box — just a clearer way to think.

active module
Physics / Kinetic energy
Physics / instrument

Kinetic energy

Watch moving energy change under steady acceleration.

Eₖ(t) = ½m(v₀ + at)²
Live 3D graph
Kinetic energy live 3D graphA two-input result surface, not a physical object. Each axis has its own scale. Held fixed: Acceleration = 1.5 m/s²; Elapsed time = 6 s. Gaps indicate undefined samples or magnitudes ≥ 10¹². Axes: Mass (kg), Initial velocity (m/s), Result (J). Kinetic energy: 1,103 J2468Mass (kg)5101520Initial velocity (m/s)02,0004,000Result (J)Current result: 1,103 J
Live inputs
24° tilt / -35° orbit / 1.00x
  • Mass (kg): 1.25 to 8.75
  • Initial velocity (m/s): 3 to 21
  • Result (J): -393.8 to 4,331
  • Live value marker
  • Result graph (independent scales)

A two-input result surface, not a physical object. Each axis has its own scale. Held fixed: Acceleration = 1.5 m/s²; Elapsed time = 6 s. Gaps indicate undefined samples or magnitudes ≥ 10¹².

Drag to orbit. Focus the graph and use arrow keys to rotate, +/− to zoom, or 0 to reset. Axis ranges adjust to keep the data in view.

Kinetic energy: 1,103 J

model notes

Each point uses the same formula as the calculator. Choose the input axes to explore a result curve or surface; the other inputs stay fixed. The amber marker shows your current calculation.

Graph updates
Live with every input
Object type
Kinetic energy
Press and drag anywhere on the model to inspect it from a new angle.

E = ½m(v₀ + at)²

Enter the known quantities. The selected unknown is calculated, not entered.

Live result
1.103e+3J
time scope
Live response · 0–6 seconds
0 s6 s1.103e+30
Export selected trace · kinetic energy (J)
final kinetic energy
1.103e+3 J
step by step
  1. 01Final velocity = 12 + 1.5 × 6 = 21 m/s
  2. 02Eₖ = ½ × 5 × (21)²
  3. 03Eₖ = 1.103e+3 J after 6 s
unit converter
Converted result
100 cm
Learn from the result

A calculator that explains the numbers

Use Vector Lab as a visual study companion: change one variable, inspect the model, and connect the substitution steps to the result. The best way to learn a formula is to see which inputs actually control it.

Study the formulas: lessons and worked examples

Start with units

Check that quantities belong together before calculating. Use the converter when a problem gives measurements in different units.

Change one input

Vary one number while holding the others steady. This makes proportional, squared, and inverse relationships easier to recognize.

Read the steps

The worked substitution shows how the formula becomes a result. Compare it with your own setup before moving to the next problem.

Are the results saved?

Recent runs and practice progress are saved locally in this browser. No account is required, and the current calculator does not send those values to a server.

Can I use it for homework?

Yes, as a study companion. Use the steps and model to understand the setup, then verify the answer with your class materials or instructor.