RC Filter Cutoff
Compute cutoff frequency (fc) and time constant (τ) for first-order RC low-pass or high-pass filters.
How to Use
- Select filter type (Low-pass or High-pass).
- Enter R and C with units.
- Optionally enter a target frequency to see reactance and attenuation guidance.
- Open “Show Work” for formulas and step-by-step math in base units.
Filter Lab View
Visual feedback for cutoff, time constant, and response at a chosen frequency.
fC
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τ
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|H(f)|
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dB
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Region:
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Show Work (step-by-step)
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Work is shown in base units (Ω, F, Hz, seconds) for clarity and consistency.
RC Filter Formulas
Cutoff frequency: fc = 1 / (2πRC)
- Time constant:
τ = RC - Capacitive reactance:
XC = 1 / (2π f C) - Magnitude (Low-pass):
|H| = 1 / √(1 + (f/fc)²) - Magnitude (High-pass):
|H| = (f/fc) / √(1 + (f/fc)²) - Decibels:
dB = 20·log10(|H|)
At
f = fc, magnitude is ~0.707 (−3 dB) for first-order filters.
FAQ
Is cutoff the same as “roll-off starts”?
Cutoff is defined at −3 dB (|H| ≈ 0.707). Roll-off begins before that, but the cutoff point is the standard reference.
How steep is a first-order RC filter?
Beyond cutoff, magnitude changes at about 20 dB/decade (≈ 6 dB/octave) for a first-order filter.
Low-pass vs high-pass—what changes?
The cutoff formula is the same (1/(2πRC)). What changes is which frequencies pass and how the transfer function is arranged.
What’s a good RC for debouncing a switch?
Common ballparks are 1–20 ms. Example: 10kΩ with 100nF gives τ = 1 ms and fc ≈ 159 Hz.
Tool Info
Last updated:
Updates may include UI improvements, unit support, and calculation edge-case handling.