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What is the spring constant?

How to find the spring constant: type the force on a spring and how far it stretches, a hanging mass and the stretch, or a mass and the time of one bounce. The spring constant calculator finds k by Hooke's law, with the energy the spring stores.

Your numbers

Units
I know
Spring constant (k), N/m
500

The spring constant is 500 N/m (2.85507 lbf/in).

Spring constant, N/mm
0.5
Spring constant, lbf/in
2.85507
Force on the spring (F), N
10
Energy stored (U), J
0.1

Spring constant (k), N/m: 500. The spring constant is 500 N/m (2.85507 lbf/in).

How to calculate

Finds a spring’s constant k by Hooke’s law, k = F ÷ x, from a force or a hanging mass and the stretch, or from the bounce period of a mass, k = 4π²m ÷ T², with the stored energy.

Example with the default inputs (I know Force and stretch, Force (F) 2.24808943099711 lbf, Stretch or compression (x) 0.78740157480315 in): The spring constant is 500 N/m (2.85507 lbf/in).

Method: k = F ÷ x (Hooke’s law), with F = m × g for a hanging mass; k = 4π² × m ÷ T² from the period of a bouncing mass. U = ½ × F × x.

  • The spring obeys Hooke’s law: the force grows in proportion to the stretch, within its elastic range.
  • The spring’s own mass is small next to the mass on it (for the bounce time).
  • Typed values are read as the exact decimals you typed; each result is rounded once to show.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. I know Hanging mass and stretch, Mass (m) 176.4 lb, Gravity (g), m/s² 9.8, Stretch or compression (x) 0.4724 in gives Force (F) 784, Spring constant (k), N/m 65,333.3, Energy stored (U), J 4.704.Source: OpenStax, College Physics 2e, §16.1 Hooke’s Law: Stress and Strain Revisited (Eq. 16.1 F = −kx; Eq. 16.4 PE = ½kx²; Example 16.1: an 80.0 kg person settles a car 1.20 cm, k = 6.53 × 10⁴ N/m; Example 16.2: k = 50.0 N/m compressed 0.150 m stores 0.563 J), https://openstax.org/books/college-physics-2e/pages/16-1-hookes-law-stress-and-strain-revisited (retrieved 2026-10-19)
  2. I know Force and stretch, Force (F) 7.5, Stretch or compression (x) 5.906 in gives Spring constant (k), N/m 50, Energy stored (U), J 0.5625, Spring constant, N/mm 0.05.Source: OpenStax, College Physics 2e, §16.1 Hooke’s Law: Stress and Strain Revisited (Eq. 16.1 F = −kx; Eq. 16.4 PE = ½kx²; Example 16.1: an 80.0 kg person settles a car 1.20 cm, k = 6.53 × 10⁴ N/m; Example 16.2: k = 50.0 N/m compressed 0.150 m stores 0.563 J), https://openstax.org/books/college-physics-2e/pages/16-1-hookes-law-stress-and-strain-revisited (retrieved 2026-10-19)
  3. I know Mass and bounce time, Mass (m) 4.409 lb, Time of one bounce (T) 1.57 s gives Spring constant (k), N/m 32.0325, Frequency (f), Hz 0.636943, Angular frequency (ω), rad/s 4.00203.Source: OpenStax, University Physics Volume 1, §15.1 Simple Harmonic Motion (Eqs. 15.9 to 15.11, T = 2π√(m/k); Example 15.2: 2.00 kg on k = 32.00 N/m has T = 1.57 s), https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion (retrieved 2026-10-19)
  4. I know Force and stretch, Force (F) 44.4822, Stretch or compression (x) 1 in gives Spring constant, lbf/in 10, Spring constant (k), N/m 1,751.27, Force (F) 44.4822.Source: NIST Special Publication 811, Appendix B.8 (1 lbf = 4.4482216152605 N, 1 in = 0.0254 m, standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19)
  5. I know Hanging mass and stretch, Mass (m) 2.205 lb, Gravity (g), m/s² 9.80665, Stretch or compression (x) 3.937 in gives Force (F) 9.80665, Spring constant (k), N/m 98.0665, Energy stored (U), J 0.490333.Source: NIST Special Publication 811, Appendix B.8 (1 lbf = 4.4482216152605 N, 1 in = 0.0254 m, standard gravity 9.80665 m/s²), https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-19); OpenStax, College Physics 2e, §16.1 Hooke’s Law: Stress and Strain Revisited (Eq. 16.1 F = −kx; Eq. 16.4 PE = ½kx²; Example 16.1: an 80.0 kg person settles a car 1.20 cm, k = 6.53 × 10⁴ N/m; Example 16.2: k = 50.0 N/m compressed 0.150 m stores 0.563 J), https://openstax.org/books/college-physics-2e/pages/16-1-hookes-law-stress-and-strain-revisited (retrieved 2026-10-19)

How it works

Hooke's law says a spring pushes back with a force in proportion to how far it is stretched or compressed: F = −kx. The spring constant k is the size of that proportion, in N/m. Choose what you know:

  • Force and stretch: k = F ÷ x.
  • Hanging mass and stretch: the weight is the force, F = m × g, so k = m × g ÷ x. Standard gravity is g = 9.80665 m/s²; type another g for another place or planet.
  • Mass and bounce time: a mass m bouncing on the spring has period T = 2π√(m ÷ k), so k = 4π² × m ÷ T².

With a force or a hanging mass, the page also shows the force F in N and the energy stored at that stretch, U = ½kx² = ½ × F × x, in J. With a bounce time it shows the angular frequency ω = 2π ÷ T in rad/s and the frequency f = 1 ÷ T in Hz.

k is shown in N/m, in N/mm (k ÷ 1,000) and in lbf/in (k × 0.0254 ÷ 4.4482216152605).

Units (exact): 1 kN = 1,000 N; 1 lbf = 4.4482216152605 N; 1 kgf = 9.80665 N; 1 mm = 0.001 m; 1 cm = 0.01 m; 1 in = 0.0254 m; 1 ft = 0.3048 m; 1 g = 0.001 kg; 1 lb = 0.45359237 kg; 1 oz = 0.028349523125 kg; 1 ms = 0.001 s; 1 min = 60 s.

Rules

  • Force from 10⁻⁹ N to 10¹² N; mass from 10⁻⁹ kg to 10¹² kg; stretch from 10⁻⁹ m to 10⁶ m; bounce time from 10⁻⁹ s to 10⁹ s; g from 10⁻⁶ to 10⁶ m/s². Limits are in SI units and include their ends; a value typed in another unit is converted first.
  • Every value is a size, so it is positive: a compression is typed as a positive x.
  • A result too large or too small to show as a number gives no answer. Within these limits it does not happen.

Output format

Every number shows to 6 significant figures, rounded half up, with trailing zeros dropped, thousands commas, and from 10¹⁵ up or below 10⁻⁶ as a × 10ⁿ. Typed values are read back as the exact decimals you typed and every unit size is exact, so with a force or a hanging mass each result is an exact fraction rounded once. From a bounce time, k carries π² and ω carries π, so they are 64-bit floats; f = 1 ÷ T is exact.

The answer sentence reads The spring constant is k N/m (k′ lbf/in)., with k and k′ written as their outputs are.

Worked examples by hand

A car's springs (OpenStax Example 16.1). An 80.0 kg person settles a car 1.20 cm, with g = 9.8 m/s². F = 80 × 9.8 = 784 N, k = 784 ÷ 0.012 = 65,333.3 N/m (OpenStax rounds to 6.53 × 10⁴ N/m). U = ½ × 784 × 0.012 = 4.704 J.

A toy gun spring (OpenStax Example 16.2). A 7.5 N force compresses the spring 0.15 m: k = 7.5 ÷ 0.15 = 50 N/m (0.05 N/mm), and U = ½ × 7.5 × 0.15 = 0.5625 J, the 0.563 J of the example.

From a bounce time (OpenStax Example 15.2). A 2.00 kg mass bounces once every 1.57 s: k = 4π² × 2 ÷ 1.57² = 78.9568 ÷ 2.4649 = 32.0325 N/m, the 32.00 N/m of the example (its 1.57 s is rounded). f = 1 ÷ 1.57 = 0.636943 Hz, ω = 2π ÷ 1.57 = 4.00203 rad/s.

A US spring rate. 10 lbf stretches a spring 1 in: k = 44.482216152605 N ÷ 0.0254 m = 1,751.27 N/m, which is exactly 10 lbf/in.

Standard gravity. 1 kg hangs from a spring and stretches it 10 cm: F = 1 × 9.80665 = 9.80665 N, k = 9.80665 ÷ 0.1 = 98.0665 N/m, U = ½ × 9.80665 × 0.1 = 0.490333 J.

Other questions people ask

How do you find the spring constant?

Divide the force by the stretch it causes: k = F ÷ x (Hooke's law). A 7.5 N force that compresses a spring 0.15 m gives k = 7.5 ÷ 0.15 = 50 N/m.

How do I find the spring constant from a hanging mass?

The hanging weight is the force: F = m × g. An 80.0 kg person who settles a car 1.20 cm gives F = 80 × 9.8 = 784 N and k = 784 ÷ 0.012 = 65,333 N/m, the 6.53 × 10⁴ N/m of OpenStax Example 16.1.

How do I find the spring constant from the period of oscillation?

A mass m bouncing on a spring has period T = 2π√(m ÷ k), so k = 4π² × m ÷ T². A 2.00 kg mass that bounces once every 1.57 s gives k = 4π² × 2 ÷ 1.57² = 32.03 N/m.

What are the units of the spring constant?

Force per length: newtons per metre (N/m) in SI. Spring makers also quote N/mm (1 N/mm = 1,000 N/m) and, in the US, pounds-force per inch (1 lbf/in = 175.127 N/m).

How much energy does a spring store?

U = ½kx², or ½ × F × x at the same stretch. A 50 N/m spring compressed 0.15 m stores ½ × 50 × 0.15² = 0.5625 J, the 0.563 J of OpenStax Example 16.2.

Why is there a minus sign in Hooke’s law?

F = −kx gives the force the spring pushes back with: it points opposite to the stretch. The spring constant itself is positive, so the page works with sizes: k = F ÷ x.