Filter Cutoff Frequency Calculator

Calculate cutoff frequency, roll-off, and phase for low-pass and high-pass RC and RL filters.

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Cutoff Frequency Marks the Transition Between Passband and Attenuation

For a first-order RC filter, the cutoff frequency occurs where the output magnitude is 1/√2 of the passband value, corresponding to −3.01 dB in power-related voltage ratios. For an RC low-pass or high-pass network, fc=1/(2πRC). Below and above this corner, the capacitor’s reactance changes relative to resistance, reshaping the signal amplitude and phase. A first-order response approaches a 20dB/decade magnitude slope in the attenuating region.

RL filters have an analogous corner fc=R/(2πL) for the appropriate topology. Cutoff does not mean the signal suddenly disappears; it is a defined point on a gradual frequency response.

RC: fc=1/(2πRC),   RL: fc=R/(2πL)
SymbolMeaningWhy it appears / units
fcCutoff frequencyHz.
RResistanceΩ.
CCapacitanceF for RC filters.
LInductanceH for RL filters.

At the first-order cutoff, the reactive and resistive magnitudes are equal in the basic network. Cascading stages can create steeper roll-off, but loading and component tolerances can shift the actual corner.

For an RC cutoff, frequency must vary inversely with both R and C. Doubling either component halves fc=1/(2πRC). A result that rises when resistance or capacitance rises indicates an inverted relationship or a metric-prefix error such as confusing µF with nF.

Worked Examples

Example 1: RC low-pass: R=10kΩ, C=1μF
f_c=1/(2π×10000×1e-6)
Result: 15.9 Hz cutoff
Audio bass filter or noise reduction
Example 2: RC high-pass: f=100Hz at f_c=15.9Hz
Gain=100/√(100²+15.9²)
Result: 0.987 (−0.11dB) — well above cutoff
Signal passes easily above cutoff
Example 3: RC low-pass
R=10kΩ, C=10nF
Result: fc≈1.59kHz
Above the corner, an ideal first-order low-pass increasingly attenuates the signal.
Example 4: Component scaling
double R with C fixed
Result: fc is halved
Cutoff is inversely proportional to the RC time constant.

Common Mistakes

⚠️
Treating −3 dB as zero output

The amplitude is about 0.707 of passband at the cutoff, not zero.

⚠️
Entering microfarads or nanofarads as farads

Convert prefixes carefully; capacitance unit errors shift cutoff by orders of magnitude.

⚠️
Ignoring source and load resistance

Real source and load impedances can alter the effective R seen by the reactive component and move the cutoff frequency.

Frequently Asked Questions

Why −20 dB/decade roll-off?
First-order RC filter: gain = 1/√(1+(f/f_c)²). At f>>f_c: gain ≈ f_c/f → halves every octave (−6 dB/octave = −20 dB/decade). Higher-order filters have steeper roll-off (2nd order: −40 dB/decade).
Practical design?
RC filters: cheap, simple, no power. Passive LC: sharper cutoff, no power, handles high current. Active op-amp filters: adjustable, can boost, zero loading effect. Choose based on application requirements.
Why is cutoff called the −3 dB point?
For voltage across the same impedance, an amplitude ratio of 1/√2 corresponds to a power ratio of 1/2, and 10log10(1/2)≈−3.01dB.
Does a low-pass filter block all frequencies above fc?
No. Attenuation increases gradually. A first-order low-pass approaches a −20dB/decade slope well above the cutoff.
How does tolerance affect cutoff frequency?
Because fc depends on component values, resistor and capacitor or inductor tolerances cause the actual corner frequency to differ from the nominal calculation.
What is the relationship between RC time constant and cutoff?
They are reciprocally related: fc=1/(2πτ). A longer time constant gives a lower frequency corner.
What does the −3 dB cutoff mean for a first-order filter?
At the cutoff frequency of a first-order low-pass or high-pass filter, the output amplitude is 1/√2≈0.707 of the passband reference and the power ratio is 1/2. That corresponds to about −3.01 dB. It does not mean the signal amplitude has fallen to one-half.

Formula Explorer connections

Interpretation: This relationship connects frequency, wavelength, speed, phase, intensity or resonance in an oscillating system. Assumption: Identify the medium, boundary conditions and reference frame. Linear waves, small amplitudes, nondispersive media or ideal resonance may be assumed.

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