Energy Calculator
Mechanical energy as one balance: kinetic plus potential on the same slip, with the conservation law worked live — including the impact speed the ledger implies when every joule cashes out as motion.
Energy Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Mechanical only — heat, sound and deformation are outside the ledger
- Uniform gravity field — no orbital or spring PE terms
In short: A 2 kg object moving at 3 m/s five metres up holds KE = ½ × 2 × 3² = 9.000000 J of motion and PE = 2 × 9.80665 × 5 = 98.066500 J of height: 107.066500 J total. Conservation says the total is the contract — drop the object and the height account drains into the motion account until the floor arrives: impact speed √(3² + 2 × 9.80665 × 5) = 10.347294 m/s. Check the arithmetic backwards: ½ × 2 × 10.347294² back-computes to the same 107.066500 J. Nothing was created on the way down; the ledger just changed departments.
Formula
E = ½mv² + mgh · impact speed = √(v² + 2gh) · the total is the contract
Kinetic energy is motion's account, potential energy height's — both in joules, both owned by the same mass. The impact speed comes from setting the whole balance to motion: ½mv²_impact = E. Air resistance is the tax collector the formula ignores; in vacuum the contract is exact.
Worked Example
- Enter mass, current speed, and height above whichever line you call zero.
- Read the split — how much is motion, how much is height right now.
- Read the impact card: the speed if ALL of it became motion on the way down.
- Change g to Moon or Mars and watch the height account re-price while motion's account never flinches.
Defaults: 9.000000 J of motion + 98.066500 J of height = 107.066500 J; impact speed 10.347294 m/s. On the Moon the same height banks only 16.2 J — the motion account did not change.
Strengths & Limits Of This Model
Where this engine is strong
- One balance for both accounts, split shown live
- Impact speed derived from the total, identity checkable on the card
Where it stops
- No drag or bounce losses
- 1-D heights — no trajectory geometry
Practical Use Cases
Teaching
conservation as one balance, not two formulas
Safety
impact speed from height and speed together
Design
energy budget for springs, drops and coasters
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.
Energy Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does the page insist on ONE total?
Because conservation is a statement about the total, not about either account. KE can be 0 and PE everything (top of a throw), or the reverse (bottom of the fall); the only number that never blinks in vacuum is their sum. Splitting energy into two formulas without the balance is how the falling projectile gets double-counted.
Where do I put the zero of height?
Anywhere — that is the point of the reference card. PE has no absolute zero; only DIFFERENCES are physical. Move your line to the tabletop and the numbers change while the impact speed does not, because the difference in height is what feeds the motion account.
Does the speed's sign matter?
Not to the ledger: kinetic energy squares the speed, so 3 m/s up and 3 m/s down bank the same joules. Direction matters to MOMENTUM — which is exactly why the two pages exist. Energy asks how much; momentum asks which way.
What does the impact card assume?
Vacuum and a rigid floor: every joule of height arrives as motion, none taxed by drag, none spent deforming. Real falls land lower and hotter; the card is the ceiling speed, the honest ideal the real world discounts.
Why is mass in every term but the total still informative?
Because the split is the information: two kilograms at height h and one kilogram at 2h carry the same PE, but their motion accounts differ and their impact speeds do not — mass cancels in free fall, which is the deepest surprise in the ledger.
Can the total be negative?
Only by choosing your reference line badly: a NEGATIVE PE below the line can outweigh motion's account. The page prints the signed truth rather than hiding it — deep mines genuinely owe energy by the book, and escape velocity is the story of paying that debt.
How does friction appear in this picture?
As a leak between accounts: sliding or air drag moves mechanical energy into heat, which this page does not track. That is why real impact speeds land under the card — the missing joules are not gone, they are in a ledger this page deliberately keeps out of scope.
Moon and Mars values — exact?
No, and the chip labels say so: 1.62 and 3.71 m/s² are fact-sheet surface values quoted to three significant figures. Standard Earth gravity (9.80665) is the only exact one — a definition by international agreement, not a measurement.