Spring Natural Frequency Calculator

How it is calculated

The tool treats the spring and mass as an ideal undamped oscillator. The angular frequency is ω = √(k ÷ m) in rad/s, the natural frequency is f = ω ÷ (2π) in hertz, and the period is T = 1 ÷ f in seconds. Here k is the spring constant in N/m and m the moving mass in kg; the formulas assume these SI units, so convert grams or lb/in before entering them. Both values must be greater than zero, otherwise no result is shown. Frequency is displayed to 3 decimals, ω to 2 and the period to 4. The tool ignores damping and the spring's own mass, so a heavy spring or strong friction will make a real system oscillate a little slower or die out.

Common mistakes

• Entering the mass in grams. A 500 g mass must be typed as 0.5; entering 500 gives 0.101 Hz instead of 3.183 Hz, a result about 31 times too low.
• Using a spring rate in N/mm or lb/in without converting. The formula expects N/m, so 2 N/mm must be entered as 2,000.
• Mixing up hertz and rad/s. A figure of 20 rad/s is only about 3.18 cycles per second; quoting ω as the frequency overstates it by 2π.
• Expecting the result to include the weight of the spring itself, or air and friction losses. The tool only uses the attached mass, so a spring that is heavy compared with the load gives a frequency slightly too high.
• Applying it to a pendulum or a beam. The pendulum depends on length and gravity, not k and m, and a beam has its own stiffness formula.