What is the potential energy?
Type a mass and a height to get its gravitational potential energy, or a spring constant and a stretch to get the energy stored in the spring. The potential energy calculator shows joules, kilojoules and foot-pounds.
- Potential energy (J)
- 490.333
The potential energy is 490.333 J (361.651 ft·lbf).
- Potential energy (kJ)
- 0.490333
- Potential energy (ft·lbf)
- 361.651
- Speed if dropped (m/s)
- 9.90285
Potential energy (J): 490.333. The potential energy is 490.333 J (361.651 ft·lbf).
How to calculate
Computes gravitational potential energy U = m g h from mass and height, or the elastic potential energy of a spring U = ½ k x², in joules, kilojoules and foot-pounds.
Example with the default inputs (Kind Gravitational, Mass 22.0462262184878 lb, Height 16.4041994750656 ft, Gravity (m/s²) 9.80665): The potential energy is 490.333 J (361.651 ft·lbf).
Method: U = m × g × h (gravitational); U = ½ × k × x² (spring).
- Gravitational: the height is measured from a chosen zero level, and g is the same over the whole height (near a planet’s surface).
- Spring: an ideal spring that follows Hooke’s law, F = k x, over the whole stretch.
- Exact unit sizes: 1 lb = 0.45359237 kg; 1 ft = 0.3048 m; 1 lbf = 4.4482216152605 N; 1 ft·lbf = 1.3558179483314004 J.
Worked examples
Each example is checked against the calculator on every build.
- Kind Gravitational, Mass 22.05 lb, Height 16.4 ft, Gravity (m/s²) 9.80665 gives Potential energy (J) 490.3325, Potential energy (kJ) 0.490333, Speed if dropped (m/s) 9.902853.Source: OpenStax, University Physics Volume 1, §8.1 Potential Energy of a System (U = m g y; U = ½ k x²), https://openstax.org/books/university-physics-volume-1/pages/8-1-potential-energy-of-a-system
- Kind Gravitational, Mass 1 lb, Height 1 ft, Gravity (m/s²) 9.80665 gives Potential energy (ft·lbf) 1, Potential energy (J) 1.355818.Source: OpenStax, University Physics Volume 1, §8.1 Potential Energy of a System (U = m g y; U = ½ k x²), https://openstax.org/books/university-physics-volume-1/pages/8-1-potential-energy-of-a-system
- Kind Spring, Spring constant 200, Spring constant unit N/m, Stretch or squeeze 3.937 in gives Potential energy (J) 1.Source: OpenStax, University Physics Volume 1, §8.1 Potential Energy of a System (U = m g y; U = ½ k x²), https://openstax.org/books/university-physics-volume-1/pages/8-1-potential-energy-of-a-system
- Kind Gravitational, Mass 154.3 lb, Height 328.1 ft, Gravity (m/s²) 1.62 gives Potential energy (J) 11,340, Potential energy (kJ) 11.34.Source: OpenStax, University Physics Volume 1, §8.1 Potential Energy of a System (U = m g y; U = ½ k x²), https://openstax.org/books/university-physics-volume-1/pages/8-1-potential-energy-of-a-system
How it works
Gravitational. U = m × g × h, with the mass m in kg, the gravity g in m/s² (9.80665 by default) and the height h in m. The page also shows the speed the mass would reach if dropped from that height with no air resistance: v = √(2 × g × h), in m/s.
Spring. U = ½ × k × x², with the spring constant k in N/m and the stretch x in m. 1 N/mm = 1,000 N/m; 1 lbf/in = 4.4482216152605 ÷ 0.0254 = 175.126835… N/m.
The energy shows in joules, kilojoules (J ÷ 1,000) and foot-pounds (J ÷ 1.3558179483314004).
Unit sizes: 1 g = 0.001 kg; 1 lb = 0.45359237 kg; 1 oz = 0.028349523125 kg; 1 t = 1,000 kg; 1 cm = 0.01 m; 1 mm = 0.001 m; 1 km = 1,000 m; 1 ft = 0.3048 m; 1 in = 0.0254 m.
Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, and every unit size is exact, so the energy is an exact fraction until it is rounded for display. The drop speed is a square root, a 64-bit float.
Output format. Every value shows 6 significant figures; values of 10¹⁵ or more, or below 10⁻⁶, show in scientific form.
When there is no answer. An energy so small that it is below the smallest number a computer can hold (about 5 × 10⁻³²⁴ J).
Assumptions
- Gravity is the same over the whole height (near a planet’s surface).
- The spring is ideal (Hooke’s law) over the whole stretch.
- Mass more than 0 and at most 10¹² kg; height 0 to 10⁷ m; gravity 0.001 to 1,000 m/s²; spring constant more than 0 and at most 10⁹ in its unit; stretch 0 to 1,000 m.
Worked examples by hand
10 kg raised 5 m on Earth. U = 10 × 9.80665 × 5 = 490.3325 J = 0.4903325 kJ. Drop speed √(2 × 9.80665 × 5) = √98.0665 = 9.90285 m/s.
1 lb raised 1 ft. U = 0.45359237 × 9.80665 × 0.3048 = 1.3558179483314004 J = 1 ft·lbf.
A 200 N/m spring stretched 10 cm. U = ½ × 200 × 0.1² = 1 J.
70 kg, 100 m up on the Moon (g = 1.62). U = 70 × 1.62 × 100 = 11,340 J = 11.34 kJ.
Other questions people ask
What is the formula for gravitational potential energy?
U = m × g × h: the mass in kilograms, times the acceleration of gravity (9.80665 m/s² on Earth), times the height in meters. A 10 kg mass raised 5 m has 10 × 9.80665 × 5 = 490.3 J.
What is the formula for spring potential energy?
U = ½ × k × x², where k is the spring constant and x the stretch or squeeze from the rest length. A 200 N/m spring stretched 0.1 m stores ½ × 200 × 0.01 = 1 J.
Where is the zero of potential energy?
Only changes in potential energy matter, so you choose the zero level: the floor, the ground, or a table top. Type the height above that level.
How fast will the object be going if it falls?
With no air resistance, all the potential energy becomes kinetic energy: m g h = ½ m v², so v = √(2gh). A mass dropped 5 m reaches √(2 × 9.80665 × 5) = 9.90 m/s, whatever its mass.
What is a foot-pound?
A foot-pound (ft·lbf) is the energy to raise 1 lb by 1 ft: 0.3048 m × 4.4482216152605 N = 1.3558 J.
Can I use it on the Moon or Mars?
Yes. Change the gravity: about 1.62 m/s² on the Moon and 3.71 m/s² on Mars. A 70 kg astronaut 100 m up on the Moon has 70 × 1.62 × 100 = 11,340 J.