Resonant frequency calculator
Enter L and C, get the resonant frequency.
How do you calculate resonant frequency?
f₀ = 1 ÷ (2π√(LC)), with L in henries and C in farads. At that frequency the inductive and capacitive reactances are equal and cancel (OpenStax University Physics).
Example
OpenStax: L = 3.00 mH and C = 800 μF resonate at about 103 Hz.
What are reactances?
The AC “resistance” of an inductor and a capacitor: X_L = 2πfL grows with frequency, X_C = 1 ÷ (2πfC) shrinks. At 60 Hz, a 10 μF capacitor has X_C = 265 Ω and a 15 mH inductor X_L = 5.7 Ω.
Where is resonance used?
Radio tuning circuits, filters and oscillators all pick out one frequency with an LC circuit.
What units can I enter?
Choose nH, μH, mH or H for inductance and pF, nF, μF or F for capacitance; the result switches between Hz, kHz, MHz and GHz.
What happens in a circuit at resonance?
In a series RLC circuit at the resonant frequency the inductive and capacitive reactances are equal, so the impedance falls to its minimum, which is just the resistance. The current is then at its maximum, the source voltage divided by R, and it is in phase with the source, so the circuit behaves as a plain resistor (OpenStax University Physics, section 15.5).
What is the Q factor?
Q measures how sharp the resonance is. For a series circuit Q = ω₀L ÷ R, where ω₀ = 2πf₀, and it also equals ω₀ divided by the bandwidth. A high Q means a narrow peak, which is why a radio can pick one station and reject its neighbors. OpenStax's example with L = 4.00 mH, C = 2.00 µF and R = 0.200 Ω has f₀ = 1,779 Hz and Q = 224.
Where the formula comes from
An inductor's reactance rises with frequency and a capacitor's falls. They are equal at one frequency, where 2πfL = 1 ÷ (2πfC); solving for f gives f₀ = 1 ÷ (2π√(LC)). Raising L or C lowers the frequency, and because the formula has a square root, quadrupling either one only halves f₀. The calculator treats the parts as ideal, with no winding resistance and no stray capacitance. In a series RLC circuit the resistance does not enter f₀; it only sets how sharp the peak is.
Worked example
OpenStax Example 15.5 uses L = 4.00 mH and C = 2.00 µF. Then √(LC) = 0.089 ms and f₀ = 1,779.4 Hz, so ω₀ = 11,180 rad/s, which is the 1.12 × 10⁴ rad/s of the text. At that frequency X_L = 44.7 Ω and X_C = 44.7 Ω, equal as they must be. With R = 0.200 Ω the circuit has Q = ω₀L ÷ R = 224 and a bandwidth of 50 rad/s, or 7.96 Hz.
Common mistakes
Prefix slips are the most common. 10 µH with 100 pF resonates at 5.03 MHz; entering the inductance as 10 mH gives 159 kHz instead. Mixing up f₀ in hertz and ω₀ in radians per second is the next, a factor of 2π. Component tolerance matters too: because f₀ varies as 1 ÷ √(LC), a capacitor that is 10% larger than marked lowers the frequency by 4.7%. And do not expect the calculated frequency to match the bench exactly in a circuit built with real coils, whose stray capacitance and winding resistance are not in the formula.
Sources: OpenStax, University Physics Volume 2, section 15.5, “Resonance in an AC Circuit,” including Examples 15.4 and 15.5 (openstax.org, read October 27, 2026). The tolerance effect follows from the formula. Related: capacitor calculator, RC time constant calculator, transformer calculator, decibel calculator. How we check our calculators.