Spring Mass Period Calculator
Enter a mass and a spring constant to get the oscillation period in seconds — plus the frequency in hertz — and see how stiffness and weight set the rhythm of the bounce.
Period and frequency at once
Enter the mass and the spring constant and the calculator returns the oscillation period (2π√(m ÷ k)) in seconds and the frequency (1 ÷ T) in hertz together.
Use SI units
Mass in kilograms and the spring constant in newtons per metre give the period in seconds — convert grams to kilograms by dividing by 1000 first.
What is the spring-mass period?
The rhythm of a bouncing spring
This spring mass period calculator finds how long one full up-and-down oscillation of a mass hanging on a spring takes. When you pull a mass on a spring and let go, it bounces back and forth in simple harmonic motion, and the time for one complete cycle is the period. It depends on just two things: the mass in kilograms and the spring constant in newtons per metre, which measures the spring's stiffness. From those two numbers the tool returns the period in seconds and the frequency — the number of bounces per second — in hertz. This is the maths behind a car's suspension, a vibrating machine mount, and the timing element in mechanical instruments.
Enter a mass in kilograms and a spring constant in newtons per metre to get the oscillation period in seconds and the frequency in hertz instantly.
The period is two pi times the square root of the mass divided by the spring constant, and the frequency is simply one divided by the period.
T = 2π × √(m ÷ k)The mass sits under a square root, so it changes the period gently: quadruple the mass and the period only doubles. The spring constant sits under the same root in the denominator, so a stiffer spring shortens the period. Use kilograms and newtons per metre and the period comes back in seconds and the frequency in hertz.
Suppose a 0.5 kg mass hangs on a spring with a spring constant of 200 N/m.
Divide mass by spring constant
0.5 ÷ 200 = 0.0025 — the ratio that sets the timing.
Take the square root
√0.0025 = 0.05 — the square root of that ratio.
Multiply by two pi
2π × 0.05 = 0.314159 s — the period. The frequency is 1 ÷ 0.314159 = 3.183099 Hz.
The formula is exact for an idealised spring, but a few real-world points are worth keeping in mind.
Ideal massless spring and small oscillations
This calculator assumes an ideal, massless spring that obeys Hooke's law and small oscillations — that is, pure simple harmonic motion. It ignores the spring's own mass, damping from friction or air resistance, and any stretching beyond the spring's elastic limit, all of which shift the real period. Keep your units consistent — kilograms for mass and newtons per metre for the spring constant — or the seconds will be wrong.