High Pass Filter Calculator — RC, RL & Op-Amp Cutoff Frequency and Gain | Metric & American

How do I use the high-pass filter calculator?

Using the high-pass filter calculator is easy! Here's how:

1. Select the filter type you're designing. The high-pass filter calculator covers the following filter types:
   • RC high-pass filter;
   • RL high-pass filter;
   • Non-inverting op-amp high-pass filter; and
   • Inverting op-amp high-pass filter.
2. Choose your unit system — metric (SI) or American. Electrical quantities use the same SI base units worldwide (ohms, farads, henries), so both systems share identical formulas; the drop-down selectors let you enter convenient sub-units such as kΩ, MΩ, μF, nF, pF, mH and μH.
3. Input the values for which you are designing. The passive RC and RL filters let you fine-tune the component values and read off the cutoff frequency, while the active (op-amp) filters also let you adjust the gain of your output through the feedback resistors.
4. Click Calculate. The tool returns the cutoff frequency f_c (Hz / kHz / MHz / GHz), the angular frequency ω_c (rad/s), the time constant τ, and — for the active filters — the passband gain in both V/V and decibels.

💡 The high-pass filter calculator lets you enter whatever values you know, and it calculates the other values for you. It adjusts its equations according to your choice of filter type.

What is a high-pass filter?

A high-pass filter is an electronic circuit that removes low-frequency components from a given AC signal. In other words, it blocks low frequencies and lets high frequencies pass through it. That's why we call it a "high-pass filter".

Its behaviour is defined by the cutoff frequency f_c (also called the corner frequency). A high-pass filter's frequency response (its Bode plot) suppresses low-frequency signals:

• Frequencies below f_c are damped (the stopband); and
• Frequencies above f_c are left untouched (the passband).

An ideal filter would drop straight down at f_c. For real-world filters, the cutoff frequency is the frequency at which the signal is damped to −3 dB — that is, the output voltage falls to 1/√2 ≈ 70.7% of the input, and the output power is halved. A first-order RC or RL high-pass filter rolls off at −20 dB/decade below the cutoff.

Different high-pass filters — passive vs. active high-pass filters

High-pass filters come in two broad families:

• Passive high-pass filters use only passive components — resistors, capacitors and inductors. They need no power supply, but they cannot amplify the signal: their passband gain is at most 1 (0 dB). The RC and RL high-pass filters are passive.
• Active high-pass filters add an operational amplifier (op-amp). Besides filtering, they provide gain, a low output impedance and buffering. The non-inverting and inverting op-amp high-pass filters are active.

How to tell high-pass and low-pass filters apart: in an RC circuit, a high-pass filter takes its output across the resistor (the capacitor blocks DC and low frequencies), while a low-pass filter takes its output across the capacitor. The capacitor is the key: at low frequencies a capacitor's reactance X_C = 1/(2πfC) is large, so little low-frequency signal reaches a resistor placed after it — only the high frequencies pass.

RC high-pass filter

The simplest high-pass filter is an RC high-pass filter: a capacitor in series with the signal followed by a resistor to ground, with the output taken across the resistor. Its cutoff frequency is:

where:

• f_c — cutoff (corner) frequency in hertz (Hz);
• R — resistance in ohms (Ω); and
• C — capacitance in farads (F).

Example: with R = 10 kΩ and C = 100 nF, the time constant is τ = R × C = 10,000 × 10⁻⁷ = 1 ms, so f_c = 1 / (2π × 0.001) ≈ 159.15 Hz. A passive RC high-pass filter has a passband gain of 1 (0 dB).

RL high-pass filter

An RL high-pass filter replaces the capacitor with an inductor. The output is taken across the inductor, whose reactance X_L = 2πfL grows with frequency — so high frequencies pass and low frequencies are blocked. The cutoff frequency is:

where:

• f_c — cutoff frequency in hertz (Hz);
• R — resistance in ohms (Ω); and
• L — inductance in henries (H).

Example: with R = 1 kΩ and L = 100 mH, τ = L / R = 0.1 / 1,000 = 0.1 ms, so f_c = 1,000 / (2π × 0.1) ≈ 1.59 kHz.

Inverting op-amp high-pass filter

An inverting op-amp high-pass filter places an input capacitor C₁ in series with the input resistor R₁, with a feedback resistor R_f (R₂) around the op-amp. The cutoff frequency is set by the input RC pair, and the passband gain is set by the resistor ratio:

The minus sign means the output is inverted (180° phase shift) relative to the input. The magnitude of the passband gain is R_f / R₁. For example, R₁ = 10 kΩ, C₁ = 100 nF and R_f = 100 kΩ give f_c ≈ 159 Hz and a gain of −10 V/V (20 dB).

Non-inverting op-amp high-pass filter

A non-inverting op-amp high-pass filter feeds the signal through a passive RC high-pass stage into the non-inverting input of the op-amp. The cutoff frequency comes from the RC stage, and the gain is set by the feedback divider R_g and R_f:

The output keeps the same phase as the input (no inversion), and the gain is always at least 1. For example, R = 10 kΩ, C = 100 nF, R_g = 10 kΩ and R_f = 100 kΩ give f_c ≈ 159 Hz and a gain of 1 + 10 = 11 V/V (≈ 20.8 dB).

FAQs

What does −3 dB mean at the cutoff frequency?

At f_c the output power is halved (3 dB below the passband). In voltage terms the output is 1/√2 ≈ 70.7% of the passband value. This is the internationally accepted definition of the cutoff (half-power) point.

What is the difference between a high-pass and a low-pass filter?

A high-pass filter passes frequencies above f_c and blocks those below it; a low-pass filter does the opposite. In an RC circuit you swap which component the output is taken across — across the resistor for high-pass, across the capacitor for low-pass.

How do capacitors create a high-pass filter?

A capacitor's reactance X_C = 1/(2πfC) is large at low frequencies and small at high frequencies. Placed in series with the signal, it blocks DC and low-frequency components while letting high frequencies through to the output resistor.

Should I choose a passive or an active high-pass filter?

Use a passive RC or RL filter when you only need to block low frequencies and don't need amplification. Use an active op-amp filter when you also want gain, buffering, or a defined output impedance.

Does the unit system change the result?

No. Electrical engineering uses SI units (Ω, F, H) worldwide, so the American and metric systems give the same cutoff frequency. The calculator converts your chosen sub-units (kΩ, μF, mH, …) to base SI units automatically.

What is the roll-off of a first-order high-pass filter?

Below the cutoff frequency a first-order (single-pole) RC or RL high-pass filter attenuates the signal by 20 dB per decade — at f_c/10 the gain is −20 dB (10% of the passband), and at f_c/100 it is −40 dB (1%).