Calculate the elastic potential energy stored in a spring using U = ½kΔx². Enter the spring constant (k) and displacement (Δx) to find the stored energy (U) — or switch modes to solve for any missing variable. Results include energy in joules, the spring force, and a visual breakdown.
Result
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Elastic Potential Energy (U)
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Spring Constant (k)
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Displacement (Δx)
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Spring Force (F = kΔx)
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Elastic potential energy is the energy stored in an elastic object — like a spring — when it is stretched or compressed from its natural (equilibrium) length. This energy is released when the spring returns to its original shape. It is a form of potential energy because it relates to the position (deformation) of the spring rather than its motion.
The formula is U = ½kΔx², where U is the elastic potential energy in joules (J), k is the spring constant in N/m (a measure of stiffness), and Δx is the displacement (stretch or compression) in meters. This equation is derived from Hooke's Law: F = kΔx.
Elastic potential energy is always positive because it depends on the square of the displacement (Δx²). Whether the spring is compressed or stretched, Δx² is always non-negative. The spring constant k is also always positive, so the product ½kΔx² is always ≥ 0.
No, the elastic potential energy stored in a spring (U = ½kΔx²) does not depend on the mass attached to it. It depends only on the spring constant k and the displacement Δx. However, the mass does affect how a spring-mass system oscillates dynamically.
Rearrange the formula to solve for k: k = 2U / Δx². Divide twice the elastic energy by the square of the displacement. For example, if U = 50 J and Δx = 0.5 m, then k = 2 × 50 / 0.25 = 400 N/m. Use the 'Solve for k' mode in this calculator to do it automatically.
Rearrange the formula to solve for Δx: Δx = √(2U / k). For example, if U = 98 J and k = 15 N/m, then Δx = √(2 × 98 / 15) = √13.07 ≈ 3.61 m. Select 'Solve for Δx' in this calculator to compute this directly.
Gravitational potential energy (GPE = mgh) depends on an object's mass, gravitational acceleration, and height above a reference point. Elastic potential energy depends on a spring's stiffness and deformation. Both are forms of stored energy, but they arise from different physical situations — gravity versus elastic deformation.
The SI unit for elastic potential energy is the joule (J). One joule equals one newton-meter (N·m) or one kg·m²/s². Other units sometimes used include kilojoules (kJ), millijoules (mJ), and in imperial contexts, foot-pounds (ft·lb) or BTU.