RC & RL Passive Filter Calculator
Low pass & high pass · RC and RL · solve for any variable · live Bode plot · IEC circuit diagram
Filter Formulas Quick Reference
fc = 1 / (2π·R·C)
τ = R · C
C = 1 / (2π·R·fc)
R = 1 / (2π·C·fc)
fc = R / (2π·L)
τ = L / R
L = R / (2π·fc)
R = 2π·L·fc
How to Calculate RC Filter Cutoff Frequency
The cutoff frequency (also called the -3dB frequency) of a first-order RC low-pass or high-pass filter is given by fc = 1 / (2π × R × C). At this frequency, the output signal is attenuated to 70.7% of its input amplitude — a 3dB reduction in power. To find fc, simply divide 1 by the product of 2π, your resistance in ohms, and your capacitance in farads.
fc = 1 / (2π × 10,000 × 0.0000001)
fc = 1 / 0.006283 = 159.15 Hz
RC vs RL Filters — When to Use Each
RC filters (Resistor-Capacitor) are by far the most common choice. They're cheap, compact, easy to design, and ideal for audio circuits, PWM smoothing, ADC anti-aliasing, and signal conditioning. Capacitors are widely available and inexpensive.
RL filters (Resistor-Inductor) are used where inductors are more practical — typically at RF frequencies where small inductors are tiny, or in power electronics where the inductor is already present (e.g., buck converter output filter). Inductors are physically larger and can saturate, so RC is preferred at audio frequencies.
What is the -3dB Point?
The -3dB point is the frequency at which a filter's output power drops to exactly half of its passband value. In voltage terms, this is 1/√2 ≈ 0.707 of the input voltage. This is called the cutoff frequency (fc) or corner frequency. Below fc for a low-pass filter (above fc for high-pass), signals pass through with minimal attenuation. Beyond the cutoff, the filter rolls off at -20 dB per decade for a first-order filter.
RC Time Constant Explained
The time constant τ (tau) = R × C tells you how quickly a capacitor charges or discharges through a resistor. After one time constant, the capacitor reaches 63.2% of its final voltage. After 5τ, it's considered fully charged (99.3%). The relationship between τ and fc is: fc = 1 / (2π·τ). A larger time constant means a lower cutoff frequency — slower response, more filtering of high frequencies.
Common Mistakes
⚠ Confusing τ and fc: The time constant τ = RC is NOT the cutoff frequency. fc = 1/(2πτ) — there's a factor of 2π between them. fc is always about 6.28× lower than 1/τ.
⚠ Unit errors: Always convert to base SI units before calculating — ohms, farads, henries, hertz. A 100nF capacitor = 100×10-9 F = 1×10-7 F. Getting this wrong by a factor of 1000 is the most common mistake.
⚠ Ignoring source impedance: Your filter's R includes any source impedance driving it. A real-world signal source with 50Ω output impedance adds to your filter's effective resistance.