HesapHanem

Spring Period Calculator

Find the period of a mass-spring oscillator.

Result

0.9935 s
1.0066 Hz

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.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    To get the spring constant for a real spring, hang a known mass and measure the stretch, then use k = m × 9.81 ÷ stretch. A 0.5 kg mass that stretches a spring by 0.245 m gives about 20 N/m, the value in the guide's example. Real springs have mass, and adding roughly a third of the spring's own mass to the load brings the predicted period closer to a stopwatch. Have you compared the tool's period with a measured one?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators