Calculator Servicescalculatorservices.com
Physics

Elastic Potential Energy

½kx² elastic PE. Free online Elastic Potential Energy. Calculate elastic potential energy online — fast, accurate, mobile-friendly, no signup needed.

PE = ½·k·x² (Hooke’s law spring).
Elastic PE
2 J

Derivation

  1. ├── 01Givenk = 100, x = 0.2
  2. ├── 02Formula{let t=e.k,a=e.x;return.5 × t × a²}
  3. ├── 03Substitute{let t=e.100,a=e.0.2;return.5 × t × a²}
  4. └── 04Compute Elastic PE2 J
Did you know?

The phrase "kinetic energy" was coined by William Thomson (Lord Kelvin) and Peter Guthrie Tait in 1867 — before that physicists called it vis viva, "living force".

§01What is

Understanding the Elastic Potential Energy

The Elastic Potential Energy computes Elastic PE from 2 inputs: spring constant (n/m), displacement (m). ½kx² elastic PE.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Elastic Potential Energy sits in that toolkit — it ½kx² elastic PE. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

{let t=e.k,a=e.x;return.5 × t × a²}

Where

k
Spring constant (N/m)
x
Displacement (m)
result
Elastic PE — in J
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Spring constant (N/m) = 100, Displacement (m) = 0.2.

  1. 01Start by noting the input — Spring constant (N/m): 100.
  2. 02Start by noting the input — Displacement (m): 0.2.
  3. 03Substitute these values into the formula: {let t=e.k,a=e.x;return.5 × t × a²}
  4. 04Compute Elastic PE: the calculator returns 2 J.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Elastic Potential Energy Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Spring constant (N/m) halved

k = 50 (from 100)

Keep every other input at its default and halve the spring constant (n/m). See how elastic pe responds.

  1. 01New Spring constant (N/m): 50
  2. 02Baseline Elastic PE: 2 J
  3. 03New Elastic PE: 1 J
  4. 04Elastic PE decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Spring constant (N/m) doubled

k = 200 (from 100)

Keep every other input at its default and double the spring constant (n/m). See how elastic pe responds.

  1. 01New Spring constant (N/m): 200
  2. 02Baseline Elastic PE: 2 J
  3. 03New Elastic PE: 4 J
  4. 04Elastic PE increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Displacement (m) halved

x = 0.1 (from 0.2)

Keep every other input at its default and halve the displacement (m). See how elastic pe responds.

  1. 01New Displacement (m): 0.1
  2. 02Baseline Elastic PE: 2 J
  3. 03New Elastic PE: 0.5 J
  4. 04Elastic PE decreases by 75% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Displacement (m) doubled

x = 0.4 (from 0.2)

Keep every other input at its default and double the displacement (m). See how elastic pe responds.

  1. 01New Displacement (m): 0.4
  2. 02Baseline Elastic PE: 2 J
  3. 03New Elastic PE: 8 J
  4. 04Elastic PE increases by 300% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
Your feedback

How useful was this calculator?

Your ratings stay in your browser — they help us learn which tools people actually rely on.

Rate it
Was this helpful?