High Pass Filter Calculator
Enter your component values to find the cutoff (-3 dB) frequency of a passive high-pass filter. Choose RC, RL, or LC topology, enter any two known values, and get the third. You also get the phase shift at the cutoff point, gain in decibels across the passband, the roll-off slope, and a live Bode magnitude plot showing gain versus frequency. All unit prefixes (pF to F, nH to H, mOhm to MOhm) are supported.
Formula
Worked example
RC example: R = 10 kOhm, C = 100 nF. fc = 1 / (2 x pi x 10000 x 0.0000001) = 159.2 Hz. At 159.2 Hz gain = -3.01 dB, phase = +45 deg. At 10 x fc = 1592 Hz gain = -0.04 dB (passband). At 0.1 x fc = 15.9 Hz gain = -20.04 dB (stopband).
What is a high-pass filter?
A high-pass filter (HPF) is a circuit that passes signals with a frequency above a specific threshold - the cutoff frequency - while attenuating signals below it. The cutoff is defined as the -3 dB point, where the output power drops to half the passband level and the voltage amplitude falls to 1/sqrt(2) (about 70.7%) of the input. High-pass filters are used to block DC bias and low-frequency hum, separate audio bands in loudspeaker crossovers, strip unwanted 50/60 Hz mains interference from sensor signals, and couple AC signals between amplifier stages.
RC vs RL vs LC - which filter type should you use?
An RC high-pass filter uses a capacitor in series with a resistor. It is the simplest and cheapest option, works well from a few hertz up to several megahertz, and is almost universally chosen for audio and signal-conditioning applications. An RL high-pass filter replaces the capacitor with an inductor in series and the resistor in parallel. Inductors are physically larger and more expensive than capacitors of equivalent impedance, but RL filters are preferred where high currents flow or where a capacitor would be impractical - such as power-line chokes. An LC filter uses both an inductor and a capacitor, making it a second-order system. The steeper 40 dB/decade roll-off is a major advantage for RF and audio crossover work, and because there is no resistive loss in the idealized LC network the passband efficiency is higher. The trade-off is cost, size, and the risk of resonant ringing near the cutoff if the Q factor is high.
How to read and use the Bode plot
A Bode magnitude plot graphs the gain in decibels on the vertical axis against frequency on a logarithmic horizontal axis. For a first-order HPF the plot is nearly flat at 0 dB well above the cutoff, passes through -3 dB exactly at fc, and then falls at a constant 20 dB per decade (6 dB per octave) as frequency decreases. A second-order LC filter has the same -3 dB point at fc but the slope below it steepens to 40 dB/decade (12 dB/octave). To use this calculator as a design tool: enter your target cutoff frequency in the "evaluate gain at frequency" field to read off the exact gain at any spot in the stopband, confirming the filter will suppress an interfering signal by the required amount.
Phase shift in high-pass filters
Every passive HPF also shifts the phase of the output relative to the input. For a first-order RC or RL filter the phase lead is +45 degrees exactly at fc, approaches +90 degrees well below fc (deep in the stopband), and decays toward 0 degrees well above fc (deep in the passband). This phase variation can cause problems in feedback control systems and in audio equipment where group-delay flatness matters. A second-order LC filter doubles these phase shifts: +90 degrees at fc, up to +180 degrees deep in the stopband. If phase fidelity matters, consider active all-pass compensation or a Bessel-response filter topology.
High-pass filter topology comparison
| Topology | Order | Roll-off slope | Cutoff formula | Typical use |
|---|---|---|---|---|
| RC | 1st | 20 dB/decade | fc = 1 / (2piRC) | Audio coupling, DC blocking, signal conditioning |
| RL | 1st | 20 dB/decade | fc = R / (2piL) | Power electronics, RF chokes, motor drives |
| LC | 2nd | 40 dB/decade | fc = 1 / (2pi sqrt(LC)) | RF filters, crossovers, power supplies |
Choosing the right filter type for your application.
Frequently asked questions
What is the -3 dB cutoff frequency?
The -3 dB frequency is the point at which the filter reduces the output power to exactly half of the passband value. In voltage terms that corresponds to an amplitude ratio of 1/sqrt(2), roughly 0.707, or -3.01 dB on a logarithmic scale. It marks the boundary between the passband and the stopband and is the standard way of specifying where a filter "begins to cut".
How do I calculate the RC high-pass filter cutoff frequency?
Use the formula fc = 1 / (2 x pi x R x C). For example, a 10 kOhm resistor paired with a 100 nF capacitor gives fc = 1 / (2 x 3.1416 x 10,000 x 0.0000001) = 159.2 Hz. This calculator does the arithmetic for you and handles unit conversions across the full range from picofarads to farads and milliohms to megohms.
What is the difference between a high-pass and a low-pass filter?
A low-pass filter passes frequencies below the cutoff and attenuates those above it. A high-pass filter does the opposite: it passes frequencies above the cutoff and attenuates those below. The mathematical relationship between them is a simple inversion of the transfer function - the low-pass uses a shunt (parallel) reactive element and the high-pass uses a series reactive element in the RC/RL/LC topology.
Why does an LC filter have twice the roll-off slope of an RC or RL filter?
Roll-off slope is proportional to filter order. An RC or RL filter is a first-order system with one reactive element, giving 20 dB per decade (6 dB per octave). An LC filter is a second-order system with two reactive elements, giving 40 dB per decade (12 dB per octave). Each additional reactive stage contributes another 20 dB/decade of slope.
Can I use this calculator to find a resistor or capacitor value for a target cutoff frequency?
Yes. Switch the "Solve for" selector to "Resistance" or "Capacitance" (or "Inductance" for RL/LC). Enter your target cutoff frequency and the known component value, and the calculator rearranges the formula algebraically to output the missing component value in the most convenient unit prefix.
What is the time constant of a high-pass filter?
For an RC filter the time constant is tau = R x C seconds, and fc = 1 / (2 x pi x tau). For an RL filter, tau = L / R. The time constant describes how quickly the filter responds to a step change: after one time constant the output has reached about 63% of its final value. A shorter tau means a higher cutoff frequency.