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Spring Period Calculator

Find the period of a mass-spring oscillator.

How it is calculated

For an ideal mass on a spring the period is T = 2π √(m / k), where m is the mass in kilograms and k is the spring constant in newtons per metre (N/m). The frequency is its reciprocal: f = 1 / T in hertz. Both are shown with four decimals.

Mass and spring constant must both be greater than zero. Notice that the amplitude and gravity do not appear in the formula: a vertical spring oscillates with the same period as a horizontal one, only around a lower equilibrium. The model ignores the mass of the spring itself and friction, so a real, heavy or damped spring will differ slightly.

Worked example

Mass 0.5 kg, spring constant 20 N/m. m / k = 0.5 / 20 = 0.025, and √0.025 ≈ 0.15811. Period T = 2π × 0.15811 ≈ 0.9935 s. Frequency f = 1 / 0.9935 ≈ 1.0066 Hz. The tool shows 0.9935 s and 1.0066 Hz.

Try this example →

Common mistakes

  • Entering the mass in grams; the formula needs kilograms, so 500 g must be typed as 0.5.
  • Confusing the spring constant with the stretch (extension); k is force per metre, not a length.
  • Thinking that a larger amplitude changes the period; for an ideal spring it does not.
  • Treating a ×4 mass as ×4 period; period scales with the square root, so 4 times the mass doubles it.

About this calculator

For a mass attached to an ideal spring undergoing simple harmonic motion, the oscillation period is T = 2π√(m/k), where m is the mass and k is the spring constant (stiffness, in N/m). The frequency is simply f = 1/T. Remarkably, the period doesn't depend on amplitude — a spring swings back and forth in the same time whether displaced a little or a lot, as long as it stays within its elastic (Hookean) range.

This relationship is a cornerstone of introductory physics for teaching oscillatory motion, and it extends directly into mechanical engineering: designing vehicle suspension systems, vibration isolators for sensitive equipment, and mechanical resonators all rely on the same mass-spring period formula to predict and tune natural frequencies. Enter the mass and spring constant to find the period and frequency.

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