Elastic Potential Energy Calculator · ½kx² Spring Energy

Elastic Potential Energy Calculator

Calculate stored spring energy from spring constant and displacement

Quick preset
Inputs
N
J
Elastic potential energy: U = ½ × k × x². Where k is the spring constant (N/m) and x is the displacement from equilibrium (m). This assumes a linear (Hooke's law) spring within its elastic limit.
Elastic Energy Result
Elastic potential energy
— J
—
🌀—
Energy (joules)
— J
Energy (millijoules)
— mJ
Energy (kilojoules)
— kJ
Energy (ft-lbs)
— ft-lbs
Force at x
— N
Force in lbf
— lbf
Equivalent height
— m
Equivalent speed
— m/s
Common spring reference — typical constants
Spring / systemSpring constantTypical displacementEnergy stored
Energy scale — what this amount compares to
Energy rangeScaleExamples
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Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.

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Elastic Potential Energy Calculator: Spring Constant and Displacement

Stretch or compress a spring, and it stores energy. This tool turns the spring constant and displacement into joules, millijoules, kilojoules, and foot-pounds. It also shows the force at that displacement, plus equivalent drop height and speed. Pick a preset like a mousetrap or car suspension, or type your own k and x. Results update as you type. No sign-up needed.

Elastic potential energy is the energy a spring holds when you bend it away from its resting shape. Engineers use it to size springs. Makers use it to compare bow limbs. Students use it to check homework. This calculator gives you that number in joules, along with the force at the same displacement and a few practical conversions. You don’t need to convert units by hand. Enter k and x in any supported unit, and the tool does the rest. The math follows Hooke’s law for a linear spring. It assumes the spring stays within its elastic limit. If you push past that point, the real world stops matching the formula. Use it for quick estimates, lab work, or comparing two spring designs side by side.

 

How to Use This Elastic Potential Energy Calculator

  1. Choose a preset from the dropdown, or leave it on Custom / manual input.

  2. Enter the spring constant in the k field. Pick N/m, N/cm, N/mm, lbf/in, or lbf/ft.

  3. Type the displacement in the x field. Units include meters, centimeters, millimeters, inches, and feet.

  4. Watch the force and energy fields update as you type.

  5. Check the hero number for stored energy in joules.

  6. Review the tile grid for millijoules, kilojoules, foot-pounds, force in lbf, equivalent height, and equivalent speed.

  7. Compare your result against the reference table for common springs.

  8. Use the Quick Examples buttons to load a ballpoint pen spring, mousetrap, car suspension, or compound bow.

 

How the Elastic Potential Energy Formula Works

Elastic potential energy is the energy stored in a spring when it is stretched or compressed, equal to half the spring constant times the square of the displacement. The formula assumes a linear spring that obeys Hooke’s law and stays inside its elastic limit.

Formula: U = ½ × k × x²

Formula: F = k × x

U is energy in joules. k is the spring constant in newtons per meter. x is displacement from equilibrium in meters. F is the force at that displacement, also in newtons.

The calculator converts every k unit to N/m and every x unit to meters before doing the math. Supported k units are N/m, N/cm, N/mm, lbf/in, and lbf/ft. Supported x units are m, cm, mm, in, and ft. If k or x is negative, the tool shows dashes and a warning. Zero is allowed. A zero spring constant or zero displacement returns zero energy.

Two extra outputs appear in the tile grid. Equivalent height is U divided by 1 kg times 9.80665 m/s². Equivalent speed is the square root of 2U divided by 1 kg. Both assume a 1 kg mass. They are reference numbers, not inputs.

 

Worked Example

Load the mousetrap preset. The spring constant is 1,200 N/m. The displacement is 0.07 m.

Step 1: Square the displacement. 0.07 × 0.07 = 0.0049 m².

Step 2: Multiply by the spring constant. 1,200 × 0.0049 = 5.88.

Step 3: Divide by 2. 5.88 ÷ 2 = 2.94 J.

The calculator shows 2.94 J. In foot-pounds, that’s about 2.17 ft-lbs. Force at that displacement is 1,200 × 0.07 = 84 N. Equivalent height for a 1 kg mass is 2.94 ÷ 9.80665 = 0.30 m. Equivalent speed is √(2 × 2.94) = 2.42 m/s.

A mousetrap stores a small amount of energy. It’s enough to snap a metal bar, but it won’t launch a heavy object far. The category label calls this “Small energy,” which lines up with hand tools and pellet guns.

Frequently Asked Questions

What is elastic potential energy?

Elastic potential energy is the energy stored in a spring or elastic material when it is stretched or compressed. It equals half the spring constant times the square of the displacement. The unit is the joule.

 

How do you calculate elastic potential energy?

Use U = ½ × k × x². Convert k to N/m and x to meters first. A 300 N/m spring displaced 0.2 m stores 0.5 × 300 × 0.04 = 6 J.

 

What is a good spring constant for a car suspension?

Typical car suspension springs run from about 20,000 N/m to 60,000 N/m. A value near 40,000 N/m is common for a passenger car. Stiffer springs reduce body roll but make the ride harsher.

 

Why is displacement squared in the spring energy formula?

Because force increases linearly with displacement. Energy is the area under the force-displacement curve, and the area of a triangle is ½ × base × height. That geometry produces x².

 

Can this elastic potential energy calculator handle pounds and inches?

Yes. The k field accepts lbf/in and lbf/ft. The x field accepts inches and feet. The tool converts both to SI units before calculating, so the result stays in joules.

 

What happens if I enter a negative displacement?

The calculator shows dashes and a warning. Displacement in the formula is squared, so a negative value would give the same energy as a positive one. But the tool treats negative input as invalid to keep the physical meaning clear.

 

Does elastic potential energy depend on the mass of the spring?

No. The formula U = ½kx² uses only the spring constant and displacement. The mass of the spring affects how fast it moves when released, not how much energy it stores.

 

How does elastic potential energy compare to kinetic energy?

They are two forms of mechanical energy. A drawn bow has elastic potential energy. When you release it, that energy becomes kinetic energy in the arrow. In an ideal system, the two amounts match.

 

What is the elastic limit of a spring?

The elastic limit is the maximum deformation a spring can take and still return to its original shape. Past that point, the spring deforms permanently. The formula U = ½kx² is only valid below the elastic limit.

 

Can I use this calculator for a compressed gas spring?

No. Gas springs have a nonlinear force curve. The ½kx² formula assumes a linear spring that follows Hooke’s law. A gas spring’s force depends on pressure and volume, not just displacement.

 

How accurate is the elastic potential energy calculator?

The math is exact for a linear spring. The accuracy of the result depends on how well your k and x values match the real spring. Manufacturer tolerances and fatigue can shift k by a few percent.

 

What is the difference between spring force and spring energy?

Spring force is k × x, measured in newtons. Spring energy is ½ × k × x², measured in joules. Force tells you how hard the spring pushes or pulls. Energy tells you how much work it can do.

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