Example 1
k = 200 N/m, x = 0.1 m → Eₛ = 1 J.
Elastic energy calculator
Type k and extension x. The calculator computes Eₛ = ½ k x². 200 N/m and 0.1 m is 1 J. Twice the x is four times the energy, not two.
Force F = kx: Hooke’s law. Work of a constant force: W = F·s.
Result
Spring constant k (N/m) and Extension x. The result shows up here.
How it works
Elastic energy grows with extension squared: Eₛ = ½ k x². At k = 200 N/m and x = 0.1 m you get 1 J, because 0.5 × 200 × 0.01. That same pair on Hooke's law gives F = 20 N. At x = 0.2 m and the same k you get 4 J, not 2 J. At k = 400 N/m and x = 0.1 m you get 2 J. At 500 N/m and 0.02 m that is 0.1 J. At 50 N/m and 0.05 m that is 0.0625 J.
At 20,000 N/m and 0.08 m, Eₛ = 64 J. At 4000 N/m and 0.25 m, Eₛ = 125 J. At 8000 N/m and 0.06 m, Eₛ = 14.4 J. At 150 N/m and 0.2 m, Eₛ = 3 J. At 300 N/m and 0.15 m, Eₛ = 3.375 J. x is squared, so the sign does not change the energy. Compress or stretch 0.1 m, same 1 J.
Stiffness k is in N/m, extension x in meters. The result is in joules. 1 J = 1 N·m. A comma and a period are the same x: 0,1 and 0.1. Typed 0 in k or x gives Eₛ = 0. Both fields need a number before 1 J can appear. The model is linear, in the elastic range, same as F = kx next door.
Force F = kx is on Hooke's law. Work of a constant force W = F·s is another calculator: for a spring the work is not F times x, it is ½kx². Kinetic energy has another unknown. Ep = m g h is yet another height.
The unit switch does not change N/m into another scale. The header symbol does not spring the joules.
Type 200 and 0.1, click Calculate, and match 1 J. Then 200 and 0.2 for 4 J. Treat 1 J as the store in the spring at 0.1 m, not as the work of a constant force on that same path.
How to use
- In the first field enter k in N/m, for example 200.
- In the second field enter x in meters, for example 0.1. The sign does not change Eₛ, because x is squared.
- Click Calculate. The calculator computes ½ k x². 200 N/m and 0.1 m give 1 J. At 0.2 m that is 4 J.
- Typed 0 gives Eₛ = 0. Both fields need a number. Twice the x is four times the energy.
- Force F = kx is on Hooke's law. A constant force along a path is on W = F·s. Here it stays ½kx².
Formula
Es = ½k x2
With Hooke’s law F = kx.
Eₛ, k, and x at a 0.1 m stretch
Spring energy here grows with x squared. 200 N/m and 0.1 m give Eₛ = 1 J; at 0.2 m you get 4 J, not 2 J. The 20 N force for that pair is on Hooke’s law.
- Eₛ
- Elastic energy: Eₛ = ½ k x². At 400 N/m and 0.1 m you get 2 J. At 20,000 N/m and 0.08 m, Eₛ = 64 J.
- k
- Stiffness in N/m. The same k = 200 at x = 0.1 m is 1 J, at x = 0.2 m is 4 J, because x is squared.
- x
- Extension in meters. The sign does not change Eₛ. Compress or stretch 0.1 m, same 1 J.
- J
- The unit of Eₛ. 1 J = 1 N·m. For a spring the work is not F times x, it is ½kx².
Real-life examples
Example 2
k = 500 N/m, x = 0.02 m.
Example 3
k = 20000 N/m, x = 0.08 m.
Example 4
k = 4000 N/m, x = 0.25 m.
Example 5
k = 50 N/m, x = 0.05 m.
Example 6
k = 8000 N/m, x = 0.06 m.
Example 7
k = 150 N/m, x = 0.2 m.
Example 8
k = 300 N/m, x = 0.15 m.
Example 9
k = 100 N/m, x = 0.03 m.
Ways to use this calculator
- You compute 1 J from k = 200 N/m and x = 0.1 m.
- You check that 0.2 m at that k is 4 J.
Frequently asked questions
How much Eₛ at k = 200 N/m and x = 0.1 m?
Eₛ = 0.5 × 200 × 0.01 = 1 J. F for that pair is 20 N.
How much at x = 0.2 m and the same k?
Eₛ = 0.5 × 200 × 0.04 = 4 J. Four times, not two. At k = 400 and x = 0.1 that is 2 J.
Which units do I type?
k in N/m, x in meters. Result in joules. 1 J = 1 N·m.
How is this different from F = kx?
Here energy ½kx². There force kx. Different quantity. The same 200 and 0.1 pair gives 1 J and 20 N.
Does negative x change Eₛ?
x² is positive. Compress or stretch 0.1 m, same Eₛ = 1 J.
Where is W = F s?
On the work page. For a spring the work is not F times x, it is ½kx².
Is 1 J 1 N·m?
Yes. 1 J = 1 N·m, so ½kx² and a force-times-distance sketch share the unit.
How much at 20,000 N/m and 0.08 m?
Eₛ = 64 J. At 4000 N/m and 0.25 m that is 125 J. At 500 N/m and 0.02 m that is 0.1 J.
Does a comma in 0.1 work?
Yes. 0,1 and 0.1 mean the same x [m]. Then ½ × k × 0.1² uses that stretch.
How much at 8000 N/m and 0.06 m?
Eₛ = 14.4 J. At 150 N/m and 0.2 m that is 3 J. At 50 N/m and 0.05 m that is 0.0625 J.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.