Three calculators, one panel.
Pick a mode below — everything recalculates live as you type, and every result explains itself.
The object's mass in any unit — converted to kilograms automatically.
Surface gravity where the object sits. Pick Custom… to use 9.8 or any other value.
Your own g in m/s² — e.g. 9.8 for quick textbook maths.
Height above your chosen zero level. Negative values are allowed — they mean below it.
Stiffness of the spring — how many newtons of force each unit of stretch costs.
How far it's stretched or squeezed from rest. Sign doesn't matter — x is squared.
The heavier mass doing the pulling — 1 Earth mass = 5.972×10²⁴ kg.
The lighter mass being pulled — 1 Moon mass = 7.348×10²² kg.
Separation of the two centres — for satellites add the planet's radius to the altitude. 1 AU = 1.496×10¹¹ m.
From question to joules in four steps.
No setup, no sign-up — the calculator behaves the same on phone, tablet and desktop.
Pick your mode
Gravitational (m·g·h) for objects at height, Spring (½k·x²) for stretched or squeezed springs, Universal (−G·m₁m₂/r) for planets, moons and orbits.
Type your values
Use whatever units you have — kg, g, lb, oz, m, cm, ft, in and more convert automatically, and gravity presets cover nine worlds.
Read the live answer
Energy appears instantly in joules, with the formula and your numbers substituted into it — plus extras like drop speed, spring force and orbital speed.
Copy the solution
One tap on COPY puts the whole worked result on your clipboard — perfect for homework, lab reports or revision notes.
Three kinds of stored energy.
Same idea every time — work done against a force gets banked as potential energy — but each situation has its own formula.
Gravitational · near a surface
Energy stored by lifting mass m to height h where gravity is g. Works whenever g is roughly constant — near a planet's surface. Feed in kg, m/s² and m and the answer lands in joules.
Elastic · a spring
Energy stored in a spring stretched or compressed by x from its natural length; k is the spring constant in N/m. Because x is squared, doubling the stretch stores four times the energy.
Universal · any two masses
The binding energy between any two masses, centre to centre, with G = 6.674×10⁻¹¹ N·m²/kg². The minus sign marks a bound pair — and near a surface this formula quietly becomes m·g·h.
Questions students actually ask.
Short, exam-friendly answers — the same physics the calculator uses.
How do I calculate gravitational potential energy?+
Multiply mass by gravity by height: PE = m × g × h. A 2 kg book lifted 2 m on Earth stores 2 × 9.81 × 2 = 39.24 J. Keep m in kg, g in m/s² and h in m so the answer lands in joules — the calculator converts lb, ft and other units for you and shows the substituted numbers.
What is the elastic potential energy of a spring?+
Use PE = ½ × k × x², where k is the spring constant in N/m and x is the stretch or compression from the natural length. A 200 N/m spring pulled 10 cm stores ½ × 200 × (0.10)² = 1 J. Stretching and compressing by the same amount store the same energy, and doubling the displacement stores four times as much.
Which units does the calculator accept?+
Mass in kg, g, lb or oz (plus Earth, Moon and Sun masses in universal mode); length in m, cm, mm, km, ft, in or miles (plus Earth radii and AU in universal mode); spring constant in N/m, N/cm, kN/m or lbf/in. Everything is converted to SI internally, and results appear in joules with kilojoule, calorie and foot-pound conversions.
What's the difference between potential and kinetic energy?+
Potential energy is stored by position or shape — a lifted weight or a compressed spring. Kinetic energy is energy of motion, KE = ½mv². Drop a lifted object and gravity converts its PE into KE; just before impact ½mv² = mgh, so v = √(2gh). The gravitational mode shows this impact speed automatically.
Why is universal gravitational potential energy negative?+
The formula −Gm₁m₂/r sets zero energy at infinite separation, so any bound pair sits below zero. The negative sign means you would have to add that much energy (its absolute value) to pull the two masses infinitely far apart. Near Earth we choose zero at the ground instead, which is why mgh comes out positive — a different reference point, not different physics.
Can potential energy be negative?+
Yes — it depends on where you set the zero. PE = mgh is measured from a reference height you choose, so an object below that level has negative PE: 1 kg sitting 2 m below the table edge holds −19.6 J relative to the tabletop. The calculator accepts negative heights and labels them so you never lose track of your reference.
Should I use 9.8 or 9.81 for g?+
Both are rounded versions of standard gravity, 9.80665 m/s², and differ by under 0.1%, so exam boards accept either. The Earth preset here uses 9.81; pick Custom… if your course wants 9.8 exactly. Other presets include the Moon at 1.62, Mars at 3.71 and Jupiter at 24.79 m/s².
Is this calculator free, and is my data sent anywhere?+
It is completely free and runs entirely in your browser — nothing you type is uploaded, logged, or sent to a server. No account, no sign-up, no limits.