Filter Cutoff Frequency Calculator

This calculator works out the cutoff frequency (−3 dB point) of a simple first-order RC or RL filter from the component values you enter. You input the resistance and capacitance (or inductance), and you get the cutoff frequency in hertz, along with the period and angular frequency. The result tells you where the filter starts to attenuate the signal by 3 dB, which is the standard reference point for filter design.

Formula

For a first-order RC low-pass or high-pass filter, the cutoff frequency is:

f_c = 1 / (2Ï€RC)

For an RL filter, the formula is:

f_c = R / (2Ï€L)

Where:

• f_c = cutoff frequency in hertz (Hz)
• R = resistance in ohms (Ω)
• C = capacitance in farads (F)
• L = inductance in henries (H)
• Ï€ ≈ 3.14159

This is the frequency at which the output power is half the input power (that’s the −3 dB point), and the output voltage is about 70.7% of the input voltage.

Worked Example

Using the default values from the calculator: R = 1000 Ω, C = 0.1 μF (which is 1 × 10�� F).

1. Multiply R and C: 1000 × 1e-7 = 1e-4
2. Multiply by 2π: 2 × 3.14159 × 1e-4 ≈ 6.28318e-4
3. Take the reciprocal: 1 / 6.28318e-4 ≈ 1591.55 Hz

The calculator rounds to two decimals, so it shows 1591.55 Hz. That means signals above this frequency are attenuated by 3 dB or more for a low-pass filter; for a high-pass filter, signals below this frequency are attenuated.

How the Cutoff Frequency Works

In a first-order RC filter, the capacitor’s impedance (reactance) changes with frequency: X_C = 1/(2πfC). At low frequencies, the capacitor looks like a high impedance, so in a low-pass configuration (resistor in series, capacitor to ground), most of the signal appears across the capacitor. As frequency rises, the capacitor’s impedance drops, shunting more signal to ground. The cutoff frequency is where the resistance equals the capacitive reactance.

At that point, the output voltage is 1/√2 ≈ 0.707 times the input, which corresponds to −3 dB in power. This is the standard definition used in audio, RF, and control systems. Some contexts (like filter design in certain audio EQ) use other reference points, but −3 dB is the most common.

Choosing Component Values

When designing a filter, you usually start with a target cutoff frequency and then pick R and C (or R and L) that are practical. Here are the key factors:

• Available components: Resistors come in standard values (e.g., 1 kΩ, 10 kΩ), and capacitors in standard values (e.g., 1 nF, 100 nF). Choose a combination that gets close to your target.
• Impedance level: Higher R means lower current draw and less loading on the source, but also higher thermal noise. Lower R reduces noise but draws more current.
• Capacitor type: Electrolytic capacitors are polarized and have high capacitance but poor high-frequency behavior. Ceramic capacitors are better for high frequencies but have lower capacitance values.
• Tolerance: Components have tolerances (often ±5% or ±10%), so the actual cutoff may vary. Use precision components if accuracy matters.

For example, to get a cutoff of 1 kHz, you could use R = 1.59 kΩ and C = 0.1 μF, or R = 15.9 kΩ and C = 0.01 μF. Both give the same product RC = 1.59e-4.

Common Mistakes and Misconceptions

One frequent error is mixing up units. Capacitance is often given in microfarads (μF) or nanofarads (nF). Remember: 1 μF = 1e-6 F, 1 nF = 1e-9 F. If you plug 0.1 μF as 0.1 instead of 1e-7, you’ll be off by a factor of a million.

Another mistake is using the formula for a second-order filter. The formula above is only for first-order (one resistor and one capacitor or inductor). For higher-order filters, the −3 dB point depends on the damping ratio and topology (e.g., Sallen-Key, Butterworth, etc.).

Also, some people confuse cutoff frequency with the resonant frequency of an LC circuit. Resonance occurs when inductive and capacitive reactances cancel, and the formula is different: f₀ = 1/(2π√(LC)).

Limits of the Formula

The RC formula assumes ideal components. Real capacitors have parasitic inductance and resistance, and real inductors have winding resistance. At very high frequencies (above a few MHz), these parasitics can shift the actual cutoff. Also, the formula assumes the filter is driven by a low-impedance source and loaded by a high-impedance load. If the load impedance is comparable to R, it will change the effective cutoff.

For audio applications, the formula is accurate enough. For RF circuits, you may need to account for component parasitics and transmission line effects.

Alternatives and Related Calculations

If you’re designing an active filter (with an op-amp), the cutoff frequency may also depend on feedback resistors. For a Sallen-Key low-pass, the cutoff is f_c = 1/(2π√(R1R2C1C2)). For a simple passive RC, this calculator is what you need.

You might also need to convert between cutoff frequency and time constant τ = RC. The cutoff frequency is f_c = 1/(2πτ). The time constant tells you how fast the capacitor charges/discharges.

If you have a target cutoff and one component value, you can rearrange the formula to find the other: R = 1/(2Ï€f_cC) or C = 1/(2Ï€f_cR).

Frequently Asked Questions

What does −3 dB mean exactly?

−3 dB means the output power is half the input power. In voltage terms, that’s about 70.7% of the input voltage. It’s the standard point where a filter is considered to start attenuating the signal.

Can I use this calculator for high-pass filters too?

Yes, the cutoff frequency of a first-order RC high-pass filter is the same formula. The difference is just the circuit configuration: high-pass has the capacitor in series and the resistor to ground. The frequency where attenuation begins is identical.

What if I have an inductor instead of a capacitor?

For an RL filter, use f_c = R/(2Ï€L). The calculator above is for RC, but you can easily swap the formula. Just enter the resistance and inductance values.

How do I choose between a low-pass and high-pass filter?

Choose based on what you want to pass. Low-pass passes frequencies below the cutoff, high-pass passes frequencies above. For example, a low-pass on a subwoofer removes treble; a high-pass on a tweeter removes bass.

Does the cutoff frequency change if I add a load?

Yes, a load resistor in parallel with the capacitor (in a low-pass) will lower the effective resistance and raise the cutoff frequency. The formula assumes an open circuit load. If your load is significant, you need to account for it.

Why is the cutoff frequency sometimes called the corner frequency?

Because on a Bode plot, the gain curve changes slope at that point, forming a “corner.� It’s also called the break frequency. Same thing.

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in r | Resistance | Ω | 1000 | 0
in c | Capacitance | F | 0.0000001 | 0
out fc | Cutoff frequency | Hz | 1 / (2 * pi * r * c) | 2
out period | Period | s | 1 / (1 / (2 * pi * r * c)) | 6
out omega | Angular frequency | rad/s | 2 * pi * (1 / (2 * pi * r * c)) | 2