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Conservation Of Energy Calculator

Work out conservation of energy instantly with clear inputs, formula shown and shareable results.

About Conservation Of Energy Calculator

With no friction the sum of potential and kinetic energy stays constant, so all the height converts to speed. Adding mgh to the initial kinetic energy and solving for v gives the arrival speed. A 3 kg mass starting 12 m up at 2 m/s arrives at about 15.4 m/s, and notice the mass cancels - a heavy and a light object arrive together.

Formulas

Energy conservation

mgh + 0.5mu^2 = 0.5mv^2

Arrival speed

v = sqrt(2gh + u^2)

Worked example

With the default values below, Conservation Of Energy Calculator returns Speed On Reaching The Bottom of 15.471. Change any input above and every figure here is recalculated in your browser.

Inputs used

Massminimum 0 kg
3 kg
Starting heightminimum 0 m
12 m
Speed at the startminimum 0 m/s
2 m/s

Results

Speed On Reaching The Bottom
15.471 m/s
Starting Potential Energy
353.04 J
Starting Kinetic Energy
6.00 J
Total Mechanical Energy
359.04 J

Step by step

  1. 1Values used
  2. 2Energy conservation
  3. 3Arrival speed
  4. 4Speed On Reaching The Bottom= 15.471 m/s
  5. 5Starting Potential Energy= 353.04 J
  6. 6Starting Kinetic Energy= 6.00 J
  7. 7Total Mechanical Energy= 359.04 J

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does mass not affect the final speed?

Because it appears in every term and cancels. The energy available scales with mass but so does the inertia to be accelerated.

What changes with friction?

Some energy becomes heat, so the arrival speed is lower. Subtract the friction work, force times distance, from the total before solving.

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