Potential Energy Calculator
Energy on layaway: what a mass at height banks under any gravity you name — with the reference-line honesty printed, because PE has no absolute zero and every number on this page is a CHOICE.
Potential Energy Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Uniform gravity — mgh, not the −GMm/r orbital law
- Gravitational lane only; no elastic ½kx² term
In short: A 70 kg climber 10 m up under Earth-standard gravity banks PE = 70 × 9.80665 × 10 = 6,864.655000 J. The same climb on Mars banks 2,597 J (37.831472% of Earth's number); on the Moon, 1,134 J (16.519403%). Nothing about the climber changed — the gravity did. And the number itself is softer than it looks: height is measured from a line YOU chose, so sea-level and basement readings disagree while describing the same climber. Only the DIFFERENCE between two heights is physics; the page's job is to keep the choice visible.
Formula
PE = mgh · only ΔPE is physical · Moon g ≈ 1.62 · Mars g ≈ 3.71 (fact-sheet values)
Gravitational potential energy is the work already done lifting the mass, held on account. Because only differences matter, every PE comes with an implicit zero — the floor, the seabed, the table. The Moon's 1.62 and Mars's 3.71 m/s² are NASA fact-sheet surface values quoted to three figures; Earth's 9.80665 is exact by definition.
Worked Example
- Enter the mass and the height above whatever line you are calling zero.
- Read the banked joules — the work the climb already cost (or the fall will refund).
- Read the worlds card for the same m and h elsewhere: the gravity is the only thing that changed.
- Move your reference line deliberately, not accidentally — the card prints which zero you chose.
Defaults: 6,864.655000 J on Earth; the same 70 kg at 10 m banks 1,134 J on the Moon and 2,597 J on Mars. Drop the reference line 10 m and Earth's number halves — same climber, same cliff, different book.
Strengths & Limits Of This Model
Where this engine is strong
- Three-worlds comparison computed live
- The reference-line choice printed, not hidden
Where it stops
- No height profile or varying-g correction
- No spring energy — by design, not omission
Practical Use Cases
Climbing & worksite
the energy a fall would refund
Planetary
same manoeuvre, three gravities
Teaching
why PE has no absolute zero
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Potential Energy Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is potential energy 'on layaway'?
Because the joules are not doing anything yet: the climb was paid for in work (the work page's F·d against gravity), and the balance sits at height until the fall, the lift's descent or the coaster's drop cashes it into motion. Nothing is lost while it waits — in vacuum, nothing is lost coming down either.
Does the zero of height matter?
It matters to the NUMBER and never to the physics. PE is defined only up to a constant: sea-level zero and basement zero give different readings of the same mass on the same shelf. Only ΔPE — the difference between two states — can be cashed, which is why this page names your line instead of pretending there is none.
Can PE be negative?
Yes — below your chosen line, the book says the mass OWES energy to get back to zero. It reads strange only if you forgot the zero was a choice: the basement is negative relative to the pavement and perfectly ordinary relative to its own floor.
Why does the Moon pay a sixth of Earth?
Because the bank rate is g: 1.62 is 16.519403% of 9.80665, so the same mass at the same height banks 16.519403% of the joules. The Apollo jumps looked easy for exactly this bookkeeping reason — gravity, not the astronaut, had changed.
How exact are the Moon and Mars values?
They are fact-sheet surface values quoted to three significant figures — 1.62 and 3.71 m/s². Real local gravity varies on both bodies as it does on Earth; the chips are for comparison, the chip label says approximate, and Earth's 9.80665 is the only exact number on the form.
What happens to the energy when the mass lands?
The account closes violently: height's joules become motion on the way down (the energy page's impact card prices the speed), then deformation, heat and sound on arrival. 'Potential' never meant harmless — it meant banked, and banks release on demand or on accident.
Is mgh valid for great heights?
Only while g is effectively constant — a few hundred metres to a few kilometres, fine; orbital heights, no. The true law is −GMm/r, and mgh is its small-height discount. Satellite work needs the full law; ladder work does not.
Where do springs fit?
They do not — this page is the gravitational lane only. Elastic PE goes as ½kx² and has its own reference (the spring's natural length); mixing the two accounts on one card is how springs get mis-anchored. The spring-constant page owns that ledger.