Example 1
L = 0.1 H, C = 1e-5 F -> f ≈ 159 Hz.
LC resonance calculator
Type L [H] and C [F]. The calculator computes f = 1/(2π√(LC)): 0.1 H and 1e-5 F is about 159 Hz, and 0.1 H and 1.013e-4 F is about 50 Hz. Zero henries or farads will not run.
Result
Inductance L (H) and Capacitance C (F). The result shows up here.
How it works
LC resonance frequency is f = 1 / (2π √(L C)). At 0.1 H and 1e-5 F you get about 159 Hz. At 1 H and 1e-6 F also about 159 Hz: the same LC. At 0.1 H and 1.013e-4 F you get about 50 Hz, mains order. At 0.01 H and 2.533e-6 F about 1000 Hz. At 0.5 H and 1e-5 F about 71.2 Hz.
The form has two fields: L in henrys and C in farads. 10 mH is 0.01. 10 µF is 1e-5. The result is in hertz, T = 1/f beside it. A comma, a period, and 1e-5 are the same C.
L and C must be positive. Zero does not sit under the square root. Both fields need a number before 159 Hz can appear. The model has no R: series without resistance. With R, series resonance is still at XL = Xc.
XL = 2πfL and Xc = 1/(2πfC) live next door. At this f they are equal. Here you want f. There you compute reactance at a known f.
0.01 H and 1e-7 F give about 5033 Hz. 0.2 H and 4.7e-6 F about 164 Hz. This calculator does not pick circuit Q. It stays with f from L and C.
Type 0.1 and 1e-5, click Calculate, and match about 159 Hz. The header symbol does not tune a coil. Treat 50 Hz from 1.013e-4 F as mains order, not as an exact filter.
How to use
- In the first field enter L in henrys, for example 0.1. 10 mH is 0.01.
- In the second field enter C in farads, for example 1e-5. 10 µF is 1e-5, not 10.
- Click Calculate. The calculator computes 1/(2π√(LC)). 0.1 H and 1e-5 F give about 159 Hz. T = 1/f sits beside it.
- L and C must be positive. Zero will not run. Both fields need a number.
- For XL and Xc, open the reactance pages. Here it stays the f where XL = Xc.
Formula
f = 1 / (2π √(L C))
L > 0, C > 0. Unit of f: Hz. T = 1/f beside it.
f, L, and C at resonance
When XL = Xc: f = 1/(2π√(LC)). 0.1 H and 1e-5 F is about 159 Hz. 0.1 H and 1.013e-4 F is about 50 Hz.
- f
- Resonance frequency [Hz]. 1 / (2π√(0.1 × 1e-5)) ≈ 159 Hz. T = 1/f is next door.
- L
- Inductance [H]. 0.1 H. Together with C under the square root.
- C
- Capacitance [F]. 1e-5 F or about 1.013e-4 F for 50 Hz. C must be positive.
- π
- The constant in 2π√(LC). Not XL or Xc on their own: here they are equal.
Real-life examples
Example 2
L = 1 H, C = 1e-6 F -> f ≈ 159 Hz.
Example 3
L = 0.1 H, C ≈ 1.013e-4 F -> f ≈ 50 Hz.
Example 4
L = 0.01 H, C = 1e-7 F -> f ≈ 5033 Hz.
Example 5
L = 1e-5 H, C = 1e-10 F -> f ≈ 5.03e6 Hz.
Example 6
L = 0.5 H, C = 1e-5 F -> f ≈ 71.2 Hz.
Example 7
L = 0.01 H, C ≈ 2.53e-6 F -> f ≈ 1000 Hz.
Example 8
L = 0.2 H, C = 4.7e-6 F -> f ≈ 164 Hz.
Ways to use this calculator
- You compute about 159 Hz from 0.1 H and 1e-5 F.
- You pick C at 0.1 H so f lands near 50 Hz.
Frequently asked questions
How much f at 0.1 H and 1e-5 F?
Frequency is about 159 Hz. You compute 1 / (2π√(0.1 × 1e-5)). That is a small LC circuit, not 50 Hz mains.
Which units do I type?
Inductance L [H], capacitance C [F]. Result f [Hz]. Type 10 µF as 1e-5, not as 10.
What if C = 0?
The calculator refuses zero farads. The square root of LC at C = 0 is zero, and you do not divide by zero.
How is this different from XL = 2πfL?
Here you solve for the f where XL = Xc. There you compute coil reactance at a given f. Different unknown.
How much at 0.1 H and 1.013e-4 F?
You get about 50 Hz, mains order. A larger C at the same L lowers the resonance.
How much at 0.01 H and 1e-7 F?
Frequency is about 5033 Hz. At 0.2 H and 4.7e-6 F you get about 164 Hz.
Does a comma in 0.1 H work?
Yes. 0.1 and 0,1 are the same L [H]. 1e-5 also works as C.
Is there R in this calculator?
No. This is ideal LC resonance, with no damping. R belongs to quality factor and bandwidth, not to this f.
How much at 0.5 H and 1e-5 F?
You get about 71 Hz. Five times L at the same C lowers f, because L sits under the square root.
How much at 0.01 H and 2.533e-6 F?
Frequency is about 1000 Hz. A kilohertz from a small coil and a few microfarads.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.