Cutoff Frequency Calculator

What the cutoff frequency calculator does

The cutoff frequency is the frequency at which a filter starts to take effect, the boundary between the frequencies it passes and those it blocks. This calculator finds it for RC and RL circuits, and can also solve backward for the resistance, capacitance, or inductance needed to set a particular cutoff.

Below is what the cutoff frequency is, the equations behind it, why it is called the corner or half-power point, and a worked example.

How to use it

1. Choose the circuit type: RC or RL.
2. Choose what to calculate and enter the known component values.
3. Press Calculate for the result, or Reset to clear it.

What the cutoff frequency is

The cutoff frequency is the frequency that marks the edge of a filter's action, the dividing line between the band of frequencies it lets through and the band it attenuates. Below or above this frequency, depending on the filter type, signals pass largely unaffected, while on the other side they are progressively weakened. It is the single most important number describing a simple filter, because it sets where the filter does its job. A filter is often specified just by its cutoff frequency and its type.

The cutoff arises from the interplay between a resistor and a frequency-dependent component, either a capacitor or an inductor. As frequency changes, the reactance of the capacitor or inductor changes, and at the cutoff frequency it reaches a particular relationship with the resistance that marks the transition. Because the reactance depends on the component values, the cutoff frequency is set entirely by the resistor and the capacitor or inductor chosen. This calculator computes that frequency for RC and RL circuits, and works in reverse to help you pick components for a target cutoff.

The equations it uses

For a resistor-capacitor circuit, the cutoff frequency is:

f_c = 1 ÷ (2πRC)

and for a resistor-inductor circuit it is:

f_c = R ÷ (2πL)

where R is the resistance, C is the capacitance, L is the inductance, and the factor of two pi comes from the angular frequency. In the RC case, larger resistance or capacitance lowers the cutoff; in the RL case, larger inductance lowers it while larger resistance raises it. The calculator applies the right formula for the circuit type, and can rearrange either one to solve for whichever component you need to reach a given cutoff frequency.

The corner and the half-power point

The cutoff frequency goes by several names that each capture something about it. It is often called the corner frequency, because on a graph of the filter's response the curve bends sharply near this frequency, like a corner, as the response changes from passing to blocking. The name evokes the shape of the filter's behaviour, flat on one side and sloping on the other, with the bend at the cutoff.

It is also called the half-power point, and this name is more precise about what happens there. At the cutoff frequency, the filter passes half the power it would at full strength, which corresponds to the output voltage falling to about 70 percent of the input. This particular point is chosen as the cutoff by convention because it marks a clear, consistent boundary. In the language of decibels, it is the point where the signal has dropped by three decibels, which is why filters are often said to have a three-decibel cutoff. The cutoff frequency this calculator finds is exactly this corner, the half-power point where the filter's action begins in earnest.

Solving for any component

Designing a filter usually means working backward: you know the cutoff frequency you want and need to choose components to achieve it. The calculator supports this by solving for any quantity in the relationship. Given a target cutoff and one component, it finds the other, so you can pick a convenient resistor and let the calculator tell you the capacitor needed, or the reverse.

This flexibility matches how filter design actually works in practice. Often one component value is fixed by what is available or by other constraints, and the second is chosen to land the cutoff in the right place. Being able to solve in either direction, and for either an RC or an RL circuit, turns the cutoff relationship from a formula you read off into a practical design aid. Whether you are analysing an existing filter to find its cutoff or designing a new one to a specification, the calculator handles both directions from the same underlying equations.

Units and precision

The calculator takes resistance in ohms and its multiples, capacitance in farads and its smaller multiples, and inductance in henries and its smaller multiples, returning the cutoff frequency in hertz and its multiples. It applies the exact RC or RL relationship and can solve for any of the quantities. The cutoff it reports is the half-power point of the filter, the frequency where its action begins, set entirely by the component values you provide.

A worked example

Suppose a resistor-capacitor filter uses a 1-kilohm resistor and a 1-microfarad capacitor.

The cutoff frequency is f_c = 1 ÷ (2πRC) = 1 ÷ (2π × 1000 × 0.000001) ≈ 159 hertz. Below this frequency the filter behaves one way and above it another, with the transition centred on 159 hertz. For a resistor-inductor filter with the same 1-kilohm resistor and a 1-millihenry inductor, the cutoff would instead be about 159 kilohertz, far higher, because the inductor is small.

Questions people ask

How do you calculate the cutoff frequency?

For an RC circuit, use f_c = 1 ÷ (2πRC); for an RL circuit, use f_c = R ÷ (2πL), from the component values.

Why is it called the corner frequency?

Because the filter's response curve bends sharply near it, like a corner, changing from passing signals to blocking them as frequency crosses the cutoff.

What is the half-power point?

The cutoff frequency, where the filter passes half the full power, with the output voltage at about 70 percent of the input. It is the same as the three-decibel point.

Can I find the components for a target cutoff?

Yes. The calculator solves in either direction, so given a desired cutoff and one component, it finds the other, which is how filters are designed in practice.

References

A quick note on where the physics comes from. The cutoff frequency of RC and RL filters and the half-power point are standard physics and electronics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 15.4, Power in an AC Circuit. https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit
2. HyperPhysics, RC Filter Circuits. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/filter.html
3. National Institute of Standards and Technology (NIST), SP 811, Guide for the Use of the International System of Units. https://www.nist.gov/pml/special-publication-811