How to use the RC Filter Cutoff Frequency Calculator
- 1. Pick the filterRC or RL, low-pass or high-pass.
- 2. Enter component valuesFor example 1k and 100n.
- 3. See fc and the plotAdd a test frequency to get the exact gain and phase there.
Cut-off frequency formula
For an RC filter, fc = 1 / (2πRC). For an RL filter, fc = R / (2πL). At fc the output is 1/√2 = 0.707 of the input, which is −3 dB, and the phase is −45° (low-pass) or +45° (high-pass).
Low-pass: |H| = 1/√(1 + (f/fc)²), phase = −tan⁻¹(f/fc). High-pass: |H| = (f/fc)/√(1 + (f/fc)²), phase = 90° − tan⁻¹(f/fc). Far from fc the gain changes by 20 dB per decade (6 dB per octave).
Worked example: R = 1 kΩ, C = 100 nF. fc = 1 / (2π × 1000 × 100×10⁻⁹) = 1,591.5 Hz. At 5 kHz the low-pass gain is 1/√(1 + 3.14²) = 0.303, which is −10.4 dB, with a phase of −72.3°.
Exam questions
- Design a low-pass filter with fc = 1 kHz using C = 0.1 µF (R = 1.59 kΩ).
- Find the attenuation at 10 fc (about −20 dB).
- Find the phase shift at the cut-off frequency.
- Find fc of an RL high-pass with R = 100 Ω and L = 10 mH.
A source resistance or load across the output changes the effective R, so in real circuits buffer the filter with an op-amp when the load is not much larger than R.
Frequently asked questions
Why is cut-off called the −3 dB point?
At fc the output power is half the input power. 10 log₁₀(0.5) = −3.01 dB, and the voltage is 0.707 of the input.
How steep is a first-order filter?
It rolls off at 20 dB per decade. For a steeper cut, cascade stages or use a second-order active filter.
Is ωc the same as fc?
No. ωc = 2π fc in rad/s. For R = 1 kΩ and C = 100 nF, ωc = 10,000 rad/s and fc = 1,591.5 Hz.
Is this tool free?
Yes. You enter your name and WhatsApp number once to see your result, and all other Uncodemy tools then open without the form.