How do you find gravitational potential energy if given weight instead of mass?

If weight W is given in Newtons, use the shortcut: GPE = W × h. This works because W = mg, so GPE = mgh = W × h. For example, a 500 N object raised 3 m has GPE = 500 × 3 = 1,500 J.

How does gravitational potential energy convert to kinetic energy?

By conservation of energy: GPE + KE = constant. When an object falls freely, lost GPE equals gained KE: mgh = ½mv². The mass cancels, giving v = √(2gh). An object falling from 10 m reaches a speed of √(2 × 9.81 × 10) = 14.0 m/s at the bottom.

How do you calculate the change in gravitational potential energy?

Use ΔGPE = mg(h₂ − h₁) = mgΔh, where h₁ is the initial height and h₂ is the final height. Positive ΔGPE means energy was stored (object rose); negative ΔGPE means energy was released (object fell). Only the height difference matters — the reference point cancels out.

What is gravitational field strength and how does it relate to g?

Gravitational field strength (g) can be expressed in two equivalent ways: as acceleration (m/s²) or as force per unit mass (N/kg). On Earth's surface, g = 9.81 m/s² = 9.81 N/kg. Both interpretations are physically correct. The field strength g = GM/R² where M is the planet's mass and R is its radius.

Gravitational Potential Energy Calculator - GPE = mgh Formula & Examples

Q: What is the formula for gravitational potential energy?

The gravitational potential energy formula is GPE = mgh, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s² on Earth), and h is height above the reference point in metres. GPE is measured in Joules (J).

Q: What are the units of gravitational potential energy?

Gravitational potential energy is measured in Joules (J). From the formula: [m]×[g]×[h] = kg × m/s² × m = kg·m²/s² = J. Other common units include kJ (1 kJ = 1000 J), cal (1 cal = 4.184 J), and kWh (1 kWh = 3,600,000 J).

Q: What is the gravitational potential energy of an object at ground level?

If ground is chosen as the reference point (h = 0), then GPE = mgh = mg × 0 = 0 J. GPE is always measured relative to a chosen reference point. The absolute value has no physical meaning — only changes in GPE (ΔGPE) matter physically.

Q: How does gravity differ on other planets?

Gravity (g) varies by planet. Values: Earth = 9.81 m/s², Moon = 1.62 m/s² (0.165g), Mars = 3.72 m/s² (0.379g), Jupiter = 24.79 m/s² (2.528g), Venus = 8.87 m/s² (0.904g), Sun = 274 m/s² (27.9g). GPE scales proportionally — the same mass at the same height has 6× more GPE on Earth than on the Moon.

Q: What is the universal gravitational constant G?

G = 6.67430×10⁻¹¹ N·m²/kg² is the universal gravitational constant that appears in Newton's law of gravitation: F = Gm₁m₂/r². It is an extremely small number, reflecting how weak gravity is compared to other fundamental forces.

Gravitational Potential Energy Calculator — GPE = mgh Formula & Examples

⚡ Gravitational Potential Energy — GPE = mgh

Select Gravity (Planet Preset):

⚖️ Enter weight (in Newtons) instead of mass — GPE = W × h directly

Mass m

Height h

Gravity g

GPE

🪐 Planet GPE Comparison — Same mass & height, different gravity

GPE for current inputs across all planets simultaneously. Notice Jupiter requires 25× more energy than the Moon!

↕️ Change in Gravitational Potential Energy — ΔGPE = mg(h₂ − h₁)

Mass m

Gravity g

Initial Height h₁

Final Height h₂

🌌 Gravitational Force — F = Gm₁m₂/r²

Universal Gravitational Constant

G = 6.67430 × 10⁻¹¹ N·m²/kg²

An extraordinarily small number — reflecting how weak gravity is compared to electromagnetic force

🌌

Famous Gravitational Forces — Quick Fill

Mass m₁

Mass m₂

Distance r (between centres)

🪐 Surface Gravity on Every Planet

Body	Mass (kg)	Radius (km)	g (m/s²)	Relative to Earth
☿ Mercury	3.301×10²³	2,440	3.70	0.377g
🟡 Venus	4.867×10²⁴	6,052	8.87	0.904g
🌍 Earth	5.972×10²⁴	6,371	9.81	1.000g
🌕 Moon	7.342×10²²	1,737	1.62	0.165g
🔴 Mars	6.417×10²³	3,390	3.72	0.379g
🟤 Jupiter	1.898×10²⁷	69,911	24.79	2.528g
🪐 Saturn	5.683×10²⁶	58,232	10.44	1.065g
🔵 Uranus	8.681×10²⁵	25,362	8.87	0.905g
🔵 Neptune	1.024×10²⁶	24,622	11.15	1.137g
☀️ Sun	1.989×10³⁰	695,700	274.0	27.94g

Gravitational Potential Energy Formula — GPE = mgh

Gravitational potential energy is the energy stored in an object due to its position above a reference point. When you lift an object, you do work against gravity — and that work is stored as GPE, ready to be released when the object falls. The gravitational potential energy formula is:

GPE = m × g × h

Also written: PE = mgh | Eₚ = mgh | U = mgh — all identical

GPE

Gravitational potential energy (Joules, J)

Mass of the object (kilograms, kg)

Gravitational acceleration (m/s² — 9.81 m/s² on Earth)

Height above chosen reference point (metres, m)

Reference point: GPE is always measured relative to a reference point — usually the ground or the lowest point in the problem. The absolute value of GPE is not physically meaningful; only changes in GPE matter. You can choose any convenient reference as h = 0.

Derived from work done: Lifting an object requires doing work against gravity: W = F × d = mg × h = mgh. This work is stored as gravitational potential energy. The mgh formula applies near Earth's surface where g is approximately constant. For large distances (space travel), use U = −Gm₁m₂/r.

Proportional relationships in GPE = mgh:

📦 Double mass → Double GPE

📏 Double height → Double GPE

🌍 Double gravity → Double GPE

🔗 GPE proportional to all three simultaneously

How to Find Gravitational Potential Energy — Step-by-Step

The four-step method for every gravitational potential energy calculation:

Identify mass m in kilograms. Convert if necessary: 1 lb = 0.4536 kg, 1 g = 0.001 kg.

Identify height h above your chosen reference point in metres. Height can be negative if below the reference.

Identify g — use 9.81 m/s² for Earth, 1.62 m/s² for Moon, 3.72 m/s² for Mars, or use the planet selector above.

Multiply: GPE = m × g × h. Result is in Joules (J) when inputs are in kg, m/s², and m.

Example 1 — Basic calculation

A 3 kg book is on a shelf 1.5 m above the floor. Find its GPE.
GPE = m × g × h = 3 × 9.81 × 1.5 = 44.1 J

Example 2 — Convert units first

A 500 g ball is thrown to a height of 8 m. Find GPE at maximum height.
Convert: m = 500 g = 0.5 kg
GPE = 0.5 × 9.81 × 8 = 39.24 J

Example 3 — Find height from GPE and mass

A 2 kg object has GPE = 196.2 J. How high is it?
Rearrange: h = GPE/(mg) = 196.2 / (2 × 9.81) = 196.2 / 19.62 = 10 m

Example 4 — Weight given instead of mass

An object weighing 400 N is raised 6 m. Find GPE.
Since Weight W = mg: GPE = W × h = 400 × 6 = 2,400 J = 2.4 kJ
When weight in Newtons is given, GPE = Weight × height directly — no need to find mass first.

Example 5 — On the Moon

A 70 kg astronaut climbs a 3 m rock on the Moon (g = 1.62 m/s²). Find GPE gained.
GPE = 70 × 1.62 × 3 = 340.2 J
Earth comparison: 70 × 9.81 × 3 = 2,060.1 J — 6.05× more energy required on Earth

Units of Gravitational Potential Energy — Joules Explained

GPE is measured in Joules (J) — the SI unit of energy. The unit derives naturally from the formula:

[GPE] = kg × m/s² × m = kg·m²/s² = J

1 Joule = 1 kg·m²/s² = 1 N·m = 1 W·s

Unit	Equivalent	Common Use
1 J	1 kg·m²/s²	SI base unit of energy
1 J	1 N·m	Force × distance
1 kJ	1,000 J	Engineering calculations
1 MJ	1,000,000 J	Large-scale energy (dams, power stations)
1 cal	4.184 J	Heat energy
1 kcal	4,184 J	Food energy (nutritional Calories)
1 BTU	1,055.06 J	Imperial heating systems
1 kWh	3,600,000 J	Electricity billing
1 eV	1.602×10⁻¹⁹ J	Atomic and particle physics

Gravitational field strength g: g = 9.81 m/s² (acceleration units) is identical to g = 9.81 N/kg (force per unit mass). Both interpretations are correct and appear in different textbooks. The N/kg notation makes it clear why multiplying by mass gives force (and thus N·m = J for GPE).

Notable GPE Values for Context:

1 kg raised 1 m on Earth

9.81 J

Person (70 kg) climbing 1 floor (3 m)

2,060 J

Car (1,500 kg) lifted 15 m (multi-storey)

220,725 J

Hydroelectric: 1 tonne water, 100 m head

981 kJ

Tidal barrage: 1 million tonnes, 5 m head

49 GJ

Change in Gravitational Potential Energy — ΔGPE = mgΔh

The change in gravitational potential energy formula is ΔGPE = mg(h₂ − h₁) = mgΔh. Only the height difference matters — the reference point cancels out completely.

ΔGPE = mg(h₂ − h₁) = mgΔh

Positive ΔGPE = energy stored (object rose) | Negative ΔGPE = energy released (object fell)

Conservation of energy connection: In the absence of friction or air resistance, ΔGPE + ΔKE = 0. When an object falls freely:

Lost GPE = Gained KE mgΔh = ½mv² v = √(2gΔh)

Example 1 — Falling object

A 1 kg ball falls from 10 m to 0 m. Find ΔGPE and final velocity.
ΔGPE = 1 × 9.81 × (0 − 10) = −98.1 J (energy released ▼)
ΔKE = +98.1 J → v = √(2 × 9.81 × 10) = 14.0 m/s

Example 2 — Roller coaster

500 kg car drops from 30 m to 3 m.
ΔGPE = 500 × 9.81 × (3 − 30) = −132,435 J = −132.4 kJ ▼
Speed: v = √(2 × 9.81 × 27) = 23.0 m/s = 82.8 km/h

Example 3 — Work to lift object

How much work to lift 25 kg from ground to 4 m shelf?
Work = ΔGPE = 25 × 9.81 × 4 = 981 J ▲

Example 4 — Reference point choice

A 5 kg mass at 3 m above floor. GPE relative to floor vs relative to 1 m table?
Relative to floor: GPE = 5 × 9.81 × 3 = 147.15 J
Relative to table: GPE = 5 × 9.81 × 2 = 98.1 J
ΔGPE between any two heights = same regardless of reference: 147.15 − 49.05 = 98.1 J ✓

Newton's Law of Gravitation — F = Gm₁m₂/r²

The formula GPE = mgh applies near Earth's surface where g is approximately constant. For large distances, gravitational force varies with distance:

F = Gm₁m₂/r²

G = 6.67430×10⁻¹¹ N·m²/kg² | Gravitational potential energy at distance r: U = −Gm₁m₂/r

The negative sign in U = −Gm₁m₂/r means GPE is zero at infinite separation and becomes more negative as objects approach — energy must be added to move objects apart. The g = 9.81 m/s² we use every day comes directly from Newton's law:

g = GM_Earth/R_Earth² = (6.674×10⁻¹¹ × 5.972×10²⁴) / (6.371×10⁶)²
= 3.986×10¹⁴ / 4.059×10¹³ = 9.82 m/s² ✓ (small variation due to Earth's non-spherical shape)

Example 1 — Earth–Moon gravitational force

F = 6.674×10⁻¹¹ × 5.972×10²⁴ × 7.342×10²² / (3.844×10⁸)²
Numerator: 6.674×10⁻¹¹ × 4.382×10⁴⁷ = 2.924×10³⁷
Denominator: (3.844×10⁸)² = 1.478×10¹⁷
F = 2.924×10³⁷ / 1.478×10¹⁷ = 1.979×10²⁰ N

Example 2 — Weight on Mars

A 70 kg person on Mars (g = 3.72 m/s²):
F = m × g = 70 × 3.72 = 260.4 N (vs 686.7 N on Earth — they weigh 38% as much)

Example 3 — Half-radius planet

Earth's mass but half the radius:
g = GM/R² = 9.81 × (1/0.5²) = 9.81 × 4 = 39.24 m/s² — 4× Earth's gravity

Gravitational Potential Energy and Kinetic Energy — Conservation of Energy

The most powerful application of GPE = mgh is its connection to kinetic energy through conservation of energy:

mgh + ½mv² = constant

Total mechanical energy is conserved in the absence of friction

GPE → KE as object falls mgh = ½mv² v = √(2gh)

Position	Height	GPE	KE	Speed
Top (released from rest)	h₀	mgh₀	0	0
Halfway down	h₀/2	mgh₀/2	mgh₀/2	√(gh₀)
Bottom	0	0	mgh₀	√(2gh₀)

Example 1 — Ball on ramp

A 3 kg ball rolls down a 5 m ramp from rest (no friction).
v = √(2 × 9.81 × 5) = √98.1 = 9.90 m/s

Example 2 — Maximum height from throw speed

Ball thrown upward at 15 m/s. Maximum height?
½mv² = mgh → h = v²/(2g) = 225/(2 × 9.81) = 11.47 m

Example 3 — Pendulum

Pendulum of length 1.2 m released from 30° to vertical. Speed at bottom?
h = L(1 − cos30°) = 1.2 × (1 − 0.866) = 1.2 × 0.134 = 0.161 m
v = √(2 × 9.81 × 0.161) = √3.16 = 1.78 m/s

Real-World Applications of Gravitational Potential Energy

💧

Hydroelectric Power

Water held in a reservoir at height h stores GPE. When released through turbines, GPE → KE → electrical energy. Power = mgh/t. The Hoover Dam generates up to 2,080 MW by releasing 13.1 million litres per second through 180 m of head — converting roughly 23 billion joules every second.

🎢

Roller Coasters

The first hill is always the tallest — it provides the initial GPE that powers the entire ride. Each subsequent hill must be shorter because friction losses mean less KE is available. Speed at any point: v = √(2g × height_dropped). A 40 m first drop gives √(2 × 9.81 × 40) = 28 m/s = 101 km/h.

🏗️

Pile Drivers

A construction pile driver raises a heavy mass to height h, then drops it. GPE = mgh converts to KE which drives piles into the ground. A 2,000 kg hammer dropped 3 m delivers GPE = 2000 × 9.81 × 3 = 58,860 J of impact energy to the pile head.

🧗

Rock Climbing Safety

A falling climber's GPE converts to force on the rope. Energy absorbed = mgh where h = twice the distance above the last anchor. Dynamic climbing ropes stretch, increasing stopping distance and reducing peak force. A 70 kg climber falling 4 m generates 70 × 9.81 × 4 = 2,746 J that the rope must absorb.

⚡

Pumped Storage Hydroelectricity

During low demand, electricity pumps water uphill (KE → GPE). During high demand, water flows back down (GPE → KE → electricity). Bath County, Virginia stores the world's largest capacity: 3,003 MW from 390 m of head — essentially a giant rechargeable battery using gravity.

⚔️

Trebuchet Physics

Medieval trebuchets converted GPE of a heavy counterweight into KE of a projectile. Energy = m_counterweight × g × h_drop. The largest trebuchets used 10-tonne counterweights dropped 4 m, storing 10,000 × 9.81 × 4 = 392,400 J — enough to hurl 150 kg stones 300 metres.

Worked Examples — All Calculation Types

1. GPE of 5 kg object at 3 m height

Formula: GPE = m × g × h
Substitute: GPE = 5 × 9.81 × 3 = 147.15 J
In kJ: 0.147 kJ | In cal: 35.17 cal

2. GPE on the Moon — 10 kg at 4 m

Formula: GPE = m × g_moon × h = 10 × 1.62 × 4 = 64.8 J
Earth comparison: 10 × 9.81 × 4 = 392.4 J — 6.06× more on Earth

3. Find height from GPE and mass

GPE = 500 J, m = 8 kg, g = 9.81 m/s²
h = GPE/(mg) = 500 / (8 × 9.81) = 500 / 78.48 = 6.37 m

4. Find mass from GPE and height

GPE = 1,000 J, h = 5 m, g = 9.81 m/s²
m = GPE/(gh) = 1,000 / (9.81 × 5) = 1,000 / 49.05 = 20.39 kg

5. GPE when given weight in Newtons

Weight W = 600 N, h = 4 m
GPE = W × h = 600 × 4 = 2,400 J = 2.4 kJ
(Since W = mg, GPE = mgh = W × h — no need to find mass separately)

6. ΔGPE for falling object and resulting velocity

m = 3 kg, falls from h = 20 m to h = 0 m
ΔGPE = 3 × 9.81 × (0 − 20) = −588.6 J (released)
v = √(2 × 9.81 × 20) = √392.4 = 19.81 m/s

7. ΔGPE for rising object and work done

m = 15 kg lifted from 2 m to 7 m
ΔGPE = 15 × 9.81 × (7 − 2) = 15 × 9.81 × 5 = 735.75 J (stored)
Minimum work required = 735.75 J

8. Gravitational force between Earth and 100 kg person

F = G × m₁ × m₂ / r² = 6.674×10⁻¹¹ × 5.972×10²⁴ × 100 / (6.371×10⁶)²
= 6.674×10⁻¹¹ × 5.972×10²⁶ / 4.059×10¹³
= 3.986×10¹⁶ / 4.059×10¹³ = 981.8 N ✓ (= 100 × 9.81 — consistent)

9. Surface gravity on Mars from Newton's law

g = GM/R² = 6.674×10⁻¹¹ × 6.417×10²³ / (3.39×10⁶)²
= 4.281×10¹³ / 1.149×10¹³ = 3.73 m/s² ✓ (matches 3.72 m/s²)

10. Speed at bottom of ramp via conservation of energy

m = 5 kg, ramp height h = 8 m (no friction)
mgh = ½mv² → v² = 2gh
v = √(2 × 9.81 × 8) = √156.96 = 12.53 m/s = 45.1 km/h

Frequently Asked Questions

What is the formula for gravitational potential energy?

The gravitational potential energy formula is GPE = mgh, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s² on Earth), and h is height above the reference point in metres. GPE is measured in Joules (J). Also written as PE = mgh, Eₚ = mgh, or U = mgh — all identical.

What are the units of gravitational potential energy?

Gravitational potential energy is measured in Joules (J). From the formula: kg × m/s² × m = kg·m²/s² = J. Common conversions: 1 kJ = 1,000 J, 1 MJ = 1,000,000 J, 1 cal = 4.184 J, 1 kWh = 3,600,000 J, 1 BTU = 1,055.06 J.

How do you find GPE if given weight instead of mass?

If weight W is given in Newtons, use the shortcut: GPE = W × h. This works because W = mg, so GPE = mgh = W × h. Example: a 500 N weight raised 3 m → GPE = 500 × 3 = 1,500 J. No need to find mass separately.

What is the difference between GPE = mgh and U = −Gm₁m₂/r?

GPE = mgh applies near a planet's surface where g is approximately constant. U = −Gm₁m₂/r is the exact formula at any distance r. The negative sign means GPE is zero at infinite distance and becomes more negative as objects approach. The mgh formula is derived from the universal law for small height changes near the surface.

How does GPE convert to kinetic energy?

By conservation of energy: GPE + KE = constant (no friction). When an object falls: mgh = ½mv², so v = √(2gh). An object falling from 10 m reaches v = √(2 × 9.81 × 10) = 14.0 m/s. The mass cancels — speed depends only on height and gravity.

What is GPE at ground level?

If ground is chosen as reference point (h = 0), then GPE = mgh = mg × 0 = 0 J. GPE is always measured relative to a chosen reference point — the absolute value has no physical meaning. Only changes in GPE (ΔGPE) are physically significant.

How does gravity differ on other planets?

Gravity varies by planet: Earth = 9.81 m/s², Moon = 1.62 m/s² (0.165g), Mars = 3.72 m/s² (0.379g), Jupiter = 24.79 m/s² (2.528g), Venus = 8.87 m/s², Sun = 274 m/s² (27.9g). GPE scales proportionally — the same mass at the same height stores 6× more GPE on Earth than on the Moon.

What is the universal gravitational constant G?

G = 6.67430×10⁻¹¹ N·m²/kg². It appears in Newton's law: F = Gm₁m₂/r². This extremely small number reflects how weak gravity is — the gravitational force between two 1 kg masses 1 m apart is only 6.674×10⁻¹¹ N, far weaker than electromagnetic forces.

How do you calculate change in gravitational potential energy?

Use ΔGPE = mg(h₂ − h₁) = mgΔh. Positive ΔGPE = energy stored (object rose); negative ΔGPE = energy released (object fell). Only the height difference matters — the reference point cancels out. For a 5 kg object rising from 2 m to 7 m: ΔGPE = 5 × 9.81 × 5 = 245.25 J.

What is gravitational field strength?

Gravitational field strength (g) can be expressed as acceleration (m/s²) or force per unit mass (N/kg) — both are equivalent. On Earth: g = 9.81 m/s² = 9.81 N/kg. The field strength g = GM/R² where M is planet mass and R is radius. This is why g varies across planets.

Gravitational Potential Energy Calculator – GPE = mgh Formula & Examples

🌍 Gravitational Potential Energy Calculator