Cutoff Frequency Calculator & Formula
- Time constant
- s
- Result
- Resistance
- 1000 Ω
- You entered
- Capacitance
- 0.000001 F
- You entered
This calculator finds the cutoff frequency of a simple RC (resistor–capacitor) or RL (resistor–inductor) filter. You enter the resistance and either the capacitance or inductance, and it returns the frequency in hertz where the output power drops to half (−3 dB).
Formula
The cutoff frequency \(f_c\) for a first-order RC low‑pass or high‑pass filter is:
\(f_c = \frac{1}{2 \pi R C}\)
- \(f_c\) – cutoff frequency in hertz (Hz)
- \(R\) – resistance in ohms (Ω)
- \(C\) – capacitance in farads (F)
For an RL filter the formula is \(f_c = \frac{R}{2 \pi L}\), where \(L\) is inductance in henries (H).
Worked Example
Using the calculator’s default values: \(R = 1000\,Ω\) and \(C = 1\,μF = 1 \times 10^{-6}\,F\).
- Multiply: \(R C = 1000 \times 1\times 10^{-6} = 1 \times 10^{-3}\,s\)
- Double with π: \(2 \pi R C = 2 \times 3.14159 \times 1\times 10^{-3} = 6.28318 \times 10^{-3}\,s\)
- Take the reciprocal: \(f_c = 1 / (6.28318 \times 10^{-3}) \approx 159.15\,Hz\)
The calculator shows 159.15 Hz, matching the step‑by‑step result. The time constant \(\tau = R C = 1\,ms\).
When to Use Cutoff Frequency
Cutoff frequency is essential in audio crossover design, signal filtering, and any circuit that needs to pass or block a range of frequencies. For a low‑pass filter, frequencies below \(f_c\) pass with little loss; above \(f_c\) they are attenuated. For a high‑pass filter, the opposite is true.
You also encounter cutoff in:
- Speaker crossovers – separating bass, midrange, and treble
- Radio and communication receivers – selecting a channel
- Power supply smoothing – removing ripple
- Sensor signal conditioning – removing noise
How to Read the Result
The cutoff frequency is the point where the output amplitude is \(1/\sqrt{2}\) (about 0.707) of the input, which corresponds to a power drop of half (−3 dB). At this frequency, the phase shift is 45°.
Below \(f_c\) in a low‑pass filter, the gain is nearly 1 (0 dB). Above \(f_c\), gain falls at 20 dB per decade (or 6 dB per octave) for a first‑order filter. That roll‑off rate is a key characteristic: a steeper roll‑off requires a higher‑order filter (more RC stages).
Choosing Component Values
To design a filter with a specific cutoff, you can rearrange the formula. For an RC filter, choose a convenient capacitor value (common values: 1 nF, 10 nF, 100 nF, 1 μF) and solve for \(R\):
\(R = \frac{1}{2 \pi f_c C}\)
Example: Want \(f_c = 1\,kHz\) with \(C = 100\,nF\)? Then \(R = 1 / (2 \pi \times 1000 \times 100\times 10^{-9}) \approx 1591.5\,Ω\). Use a standard 1.6 kΩ resistor.
For an RL filter, choose a standard inductor and solve for \(R\). Inductors are less common and often bulkier, so RC filters are usually preferred in practice.
Common Mistakes and Limitations
- Unit errors: Capacitance in μF must be converted to farads (1 μF = 1e−6 F). Inductance in mH must be converted to henries (1 mH = 1e−3 H).
- Confusing low‑pass and high‑pass: The formula is the same, but the component placement differs. In an RC low‑pass, the resistor is in series and the capacitor to ground; in a high‑pass, they swap.
- Ignoring source and load resistance: The formula assumes an ideal source and an unloaded output. Real circuits have source impedance and load resistance that shift the actual cutoff.
- Using the −3 dB point for all filters: For Butterworth or other filter types, the definition may differ, but for a first‑order RC/RL filter, −3 dB is standard.
Alternatives and Related Concepts
If you need a sharper roll‑off, consider a second‑order filter (two RC stages) which gives 40 dB/decade. Active filters using op‑amps can provide gain and steeper slopes without inductors. For digital signals, you might use a software low‑pass filter (e.g., moving average) instead of an analog one.
The cutoff frequency is also related to the time constant \(\tau = RC\): \(f_c = 1/(2\pi\tau)\). In control systems, the same concept appears as the bandwidth or corner frequency.
Frequently Asked Questions
What does −3 dB mean?
−3 dB corresponds to a power ratio of 0.5 (half). In voltage terms, it’s \(1/\sqrt{2}\) ≈ 0.707 times the input. It’s the standard definition for cutoff because it marks the point where the output power drops by half.
Can I use this calculator for a high‑pass filter?
Yes. The cutoff frequency formula is identical for low‑pass and high‑pass RC filters. The calculator gives the frequency where the transition occurs; the circuit topology determines which frequencies are passed.
How do I convert μF to farads?
Multiply by 10��. For example, 0.1 μF = 0.1 × 10�� = 1×10�� F. In the calculator, you can enter 1e-7 directly.
What if I have an inductor instead of a capacitor?
Use the RL formula \(f_c = R/(2\pi L)\). The calculator above is for RC; you can adapt it by entering the inductance value in henries and adjusting the formula manually, or use a dedicated RL calculator.
Why is my measured cutoff different from the calculated one?
Component tolerances, parasitic capacitance, and source/load resistances all affect the real cutoff. Also, the formula assumes an ideal capacitor and resistor; real components have small reactance and resistance variations.