High Pass Filter Calculator

Compute cutoff frequency (–3 dB point), gain (dB) & phase shift for passive RC or RL high‑pass filters. Visualize magnitude Bode plot, design crossovers, or analyze signal conditioning circuits.

1 μF = 1e-6 F
? Audio HPF (80 Hz) : R=1kΩ, C=1.99μF
? Standard RC : R=1kΩ, C=1μF (159 Hz)
?️ RL Crossover : R=8Ω, L=1.5mH (848 Hz)
? Subsonic : R=10kΩ, C=0.22μF (72.3 Hz)
Local computation: All calculations run inside your browser. No data is sent to any server.

1st Order High‑Pass Filter: Theory & Practical Insight

A high-pass filter (HPF) attenuates frequencies below the cutoff frequency \(f_c\) and passes frequencies above it. The simplest passive implementations are the RC and RL networks. These filters are fundamental in audio crossovers, signal conditioning, DC blocking, and biomedical instrumentation. The cutoff frequency is defined where the output power drops by half (−3 dB relative to the passband).

For RC: \( f_c = \frac{1}{2 \pi R C} \)    |    For RL: \( f_c = \frac{R}{2 \pi L} \)

The voltage transfer function magnitude and phase are derived from the voltage divider principle:
\( H(j\omega) = \frac{j\omega RC}{1 + j\omega RC} \) (RC case). The magnitude in dB: \( |H|_{dB} = 20 \log_{10}\left( \frac{f/f_c}{\sqrt{1+(f/f_c)^2}} \right) \). Phase angle: \( \phi = 90^\circ - \arctan(f/f_c) \). Above \( f_c \), gain approaches 0 dB; below \( f_c \), roll‑off is +20 dB/decade.

Design Methodology & Key Specifications

  • Cutoff frequency selection: Choose \( f_c \) based on the lowest frequency to preserve. For example, in audio, a 80 Hz HPF removes rumble while preserving voice/music fundamentals.
  • Impedance matching: Ensure load impedance is much larger than filter output impedance to avoid loading effects. Our calculator assumes ideal source and load.
  • Component tolerances: Use 1% resistors and 5–10% capacitors for predictable cutoff.

For real‑world circuits, also consider the source and load impedances: the formulas above assume an ideal voltage source and infinite load. When the load impedance is comparable to R, the actual cutoff frequency shifts – our interactive plot helps you visualise the ideal response as a first approximation.

Real‑World Applications

Audio crossover networks
Tweeter protection: a high-pass filter prevents low‑frequency energy from damaging high‑frequency drivers. Typical crossover: 2.2 µF + 8Ω yields ≈ 9 kHz.
Biomedical (ECG/EEG)
Remove baseline wander and DC offset. HPF with 0.05 Hz – 0.5 Hz cutoff stabilizes signal acquisition.
Engineering insight – Active vs Passive: While this calculator focuses on passive RC/RL filters, active high-pass filters using op-amps provide gain and buffering. The same transfer function principles apply, but cutoff calculation remains identical for first-order. High‑pass filters are also essential in RF receivers to block DC offsets after mixing, preventing amplifier saturation.

Step‑by‑Step Calculation & Bode Interpretation

Our solver determines \(f_c\) from your R and C (or L). It then reconstructs the Bode magnitude plot over a frequency range spanning 0.01×\(f_c\) to 100×\(f_c\) on a logarithmic scale. This reveals the characteristic +20 dB/decade slope below cutoff and the flat passband. The –3 dB line crossing at \(f_c\) validates the design. Use the test frequency input to evaluate gain or phase at any specific point – ideal for checking attenuation at undesired harmonics.

Example: Designing a Subsonic Filter for Turntables

Vinyl records may suffer from low-frequency rumble (below 20 Hz). Using R = 10 kΩ and C = 0.79 μF yields \(f_c \approx 20\) Hz. This filter attenuates rumble by –20 dB at 2 Hz without affecting audible spectrum. Our tool instantly verifies this design, giving engineers confidence before prototyping.

Frequently Asked Questions

Both are first-order high-pass filters. RC uses a resistor and capacitor; RL uses a resistor and inductor. The RC filter is more common due to lower cost and size, but RL filters are used in power applications and RF circuits where inductors are practical.

At \(f = f_c\), the magnitude of the transfer function is \(1/\sqrt{2} \approx 0.707\). Converting to decibels: \(20\log_{10}(0.707) = -3.01\) dB. This marks the half-power point, a standard bandwidth definition.

The plot uses the exact transfer function evaluated at 200 logarithmically spaced points, ensuring high visual accuracy. It matches theoretical curves within 0.1 dB.
References & Further Reading: All About Circuits – High-pass Filters, Horowitz & Hill “The Art of Electronics”, Wikipedia: High-pass filter.
Reviewed by GetZenQuery tech team — last update May 2026.