Spring Natural Frequency Calculator

About this calculator

Every undamped mass-spring system oscillates at a characteristic natural frequency, given by f = (1/2π)√(k/m), where k is the spring constant and m is the attached mass. This calculator derives that frequency along with the angular frequency ω = √(k/m) and the oscillation period T = 1/f, the three interlinked quantities that describe how fast the system bounces once displaced and released.

Natural frequency is a foundational concept in mechanical and structural engineering, used in vibration analysis to predict resonance — the dangerous amplification that occurs when an external driving force matches a system's natural frequency — and in the design of suspensions, vibration isolators, and precision instruments. Mechanical engineers use it early in design to keep a component's natural frequency safely away from expected operating or excitation frequencies.