Resonant Frequency Calculator

An LC circuit naturally oscillates at its resonant frequency.

How the Math Works

The resonant frequency of an LC circuit is determined by the formula f₀ = 1 ÷ (2π·√(L·C)), where L represents inductance in henries and C represents capacitance in farads. This equation calculates the natural frequency at which energy oscillates between the inductor's magnetic field and the capacitor's electric field. The square root of the product L·C gives the time constant governing the oscillation period, while the factor 2π converts this into cycles per second (hertz). At resonance, the circuit's inductive and capacitive reactances cancel each other, resulting in minimum impedance and maximum current flow.

Practical Applications

To use this calculation in practical circuit design, measure or select your desired inductor and capacitor values, then input them into the formula or calculator. For example, if you have a 10 µH inductor and 100 ±F capacitor, the resonant frequency calculates to approximately 159 kHz. Engineers apply this when designing radio tuners, filter circuits, and oscillators, adjusting component values to achieve specific frequencies for communication systems, audio equipment, or power supplies. You can also work backward: knowing your target frequency, calculate the required L·C product to select appropriate components.

Day-to-Day Use

While you may not calculate resonant frequencies daily, this principle enables many technologies you interact with regularly. Your smartphone's Wi-Fi and cellular antennas are tuned using LC circuits to resonate at specific frequencies, ensuring reliable communication. Radio stations use this concept to broadcast and receive signals, allowing you to listen to music and news. Even wireless charging pads for electric toothbrushes and phones rely on resonant frequency matching between transmitter and receiver coils. Understanding this helps explain why certain electronic devices work seamlessly together and how wireless technologies connect our modern world.

Worked example

10 mH, 1 µF → about 1592 Hz.

FAQ