Corner Frequency Calculator: RC Filter Cutoff

This corner frequency calculator determines the cutoff frequency (also called the corner frequency or -3 dB point) of a simple RC (resistor-capacitor) filter. You enter the resistance and capacitance values, and it returns the frequency in hertz where the filter’s output power drops to half its input power, which is a standard measure of a filter’s bandwidth limit.

Formula

The corner frequency of a first-order RC filter is given by:

f_c = 1 / (2πRC)

Where:

• f_c is the corner frequency in hertz (Hz).
• R is the resistance in ohms (Ω).
• C is the capacitance in farads (F).
• π is the mathematical constant approximately equal to 3.14159.

The product RC is called the time constant (τ) of the circuit, measured in seconds. The corner frequency is the reciprocal of 2π times the time constant.

Worked Example

Using the default values from the calculator: R = 1000 Ω and C = 0.1 µF (which is 0.1 × 10^-6 F = 1 × 10^-7 F).

1. Calculate the time constant: τ = R × C = 1000 × 1 × 10^-7 = 1 × 10^-4 s (0.0001 s).
2. Multiply by 2π: 2πτ = 2 × 3.14159 × 1 × 10^-4 ≈ 6.28318 × 10^-4 s.
3. Take the reciprocal: f_c = 1 / (6.28318 × 10^-4) ≈ 1591.5 Hz.

The calculator rounds to one decimal place, giving a corner frequency of 1591.5 Hz and a time constant of 0.000100 s (shown as 0.000100 with six decimals).

What the Corner Frequency Means

In a low-pass RC filter, frequencies below the corner frequency pass through with little attenuation, while frequencies above it are progressively reduced. At the corner frequency itself, the output voltage amplitude is 70.7% of the input (that is, 1/√2), and the output power is half the input power. This is why the corner frequency is also called the -3 dB point: in decibels, 20 log₁₀(1/√2) ≈ -3.01 dB.

For a high-pass RC filter, the roles are reversed: frequencies above the corner frequency pass, and lower frequencies are attenuated. The formula is identical; only the circuit topology changes (the output is taken across the resistor instead of the capacitor).

How to Choose R and C for a Desired Cutoff

Often you know the cutoff frequency you need and must pick component values. Rearranging the formula gives RC = 1 / (2πf_c). For example, to get a 1 kHz cutoff:

• RC = 1 / (2π × 1000) ≈ 1.59 × 10^-4 s.
• If you choose R = 1.59 kΩ, then C = 1.59 × 10^-4 / 1590 ≈ 1 × 10^-7 F = 0.1 µF.
• If you choose R = 10 kΩ, then C = 1.59 × 10^-4 / 10000 = 1.59 × 10^-8 F ≈ 16 nF.

In practice, pick a standard capacitor value first (like 0.01 µF, 0.1 µF, 1 µF) and then calculate the resistor needed. Resistors come in more precise standard values, so this approach usually yields a closer match.

Common Mistakes and Misconceptions

• Unit mix-ups: The formula requires capacitance in farads, but most capacitors are labeled in microfarads (µF), nanofarads (nF), or picofarads (pF). Forgetting to convert to farads is the most frequent error. Remember: 1 µF = 1×10^-6 F, 1 nF = 1×10^-9 F, 1 pF = 1×10^-12 F.
• Confusing -3 dB with half voltage: The -3 dB point is half power, not half voltage. The voltage is 70.7% of the input, which surprises many beginners.
• Assuming a sharp cutoff: A first-order RC filter has a gentle roll-off of 20 dB per decade (or 6 dB per octave) above the corner frequency. It does not block all higher frequencies abruptly.
• Loading effects: The formula assumes an ideal voltage source and no load on the output. In real circuits, the input impedance of the next stage can shift the effective corner frequency.

Comparison with Other Filter Types

The RC filter is the simplest first-order filter. Higher-order filters (e.g., Sallen-Key, Butterworth, Chebyshev) use multiple RC stages or op-amps to achieve a steeper roll-off. For a second-order Butterworth filter, the corner frequency formula is different and involves the natural frequency ω₀ = 1/√(R₁R₂C₁C₂), and the -3 dB point depends on the damping ratio. The simple RC formula applies only to first-order filters with a single resistor and capacitor.

Also, RL filters (resistor-inductor) have the same corner frequency formula but with the time constant L/R instead of RC. The calculator here is specific to RC circuits.

Limits and Practical Notes

The formula assumes ideal components: a resistor with no parasitic inductance and a capacitor with no equivalent series resistance (ESR). At very high frequencies (above a few MHz), parasitic effects become significant, and the actual cutoff may deviate. For most audio and low-frequency applications, the ideal formula is accurate enough.

Also, the corner frequency is defined for a sinusoidal input. For square waves or other waveforms, the concept of cutoff still applies, but the output shape changes in a more complex way. The time constant τ = RC also tells you how quickly the capacitor charges or discharges: after one time constant, the voltage reaches about 63.2% of its final value.

Frequently Asked Questions

What is the difference between corner frequency and cutoff frequency?

They are the same thing. Both terms refer to the frequency at which the output power drops to half the input power (-3 dB). Some fields prefer “corner frequency” because it is the point where the asymptotic lines of the Bode plot meet at a corner; others use “cutoff frequency” because it marks the edge of the passband.

Can I use this calculator for a high-pass filter?

Yes. The corner frequency formula is identical for high-pass and low-pass RC filters. The only difference is which component you take the output across: for low-pass, output across the capacitor; for high-pass, output across the resistor.

What if I have a resistor and capacitor in series but no ground?

The formula still applies as long as you have a single RC network. The corner frequency depends only on the R and C values, not on the reference point. However, in a real circuit, the source and load impedances affect the response, so the simple formula assumes ideal conditions.

How do I convert farads to microfarads?

1 farad = 1,000,000 microfarads (µF). So to convert from µF to F, divide by 1,000,000. For example, 0.1 µF = 0.1 / 1,000,000 = 1 × 10⁻⁷ F. The calculator does this conversion automatically when you enter the capacitance in µF.

Why is the corner frequency at -3 dB and not -6 dB?

The -3 dB point corresponds to half power, which is the standard definition for bandwidth in electronics. A -6 dB point would be quarter power, which is a different metric. The factor 1/√2 in voltage comes from the fact that power is proportional to voltage squared: (1/√2)² = 1/2.

Does the corner frequency change if I use a potentiometer as the resistor?

Yes, if you adjust the potentiometer, the resistance changes, and therefore the corner frequency changes. That is a common way to make a tunable filter. The formula remains the same; you just use the current resistance value.

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in r | Resistance | Ω | 1000 | 0
in c | Capacitance | µF | 0.1 | 0
out fc | Corner frequency | Hz | 1 / (2 * pi * r * c * 1e-6) | 1
out tau | Time constant | s | r * c * 1e-6 | 6