What is the RC Low-Pass & High-Pass Filter Calculator?
This calculator models one passive first-order RC section with an ideal zero-resistance source and no output load. Low-pass output is measured across the capacitor; high-pass output is measured across the resistor. Both arrangements have the same cutoff formula, while their gain and phase responses differ.
Use it to estimate cutoff from R and C or choose one component for a target cutoff. An optional test frequency adds the sinusoidal voltage magnitude ratio, gain in decibels relative to unity, and output phase. The RC Time Constant Calculator remains the separate tool for capacitor charging and discharging over time.
Affiliate disclosure: As an Amazon Associate I earn from qualifying purchases.
Optional resistor assortments (paid link) can help compare nominal component values. Check actual tolerance and ratings; no purchase is required to use this tool.
How to use the RC low-pass or high-pass filter calculator
- Choose Low-pass or High-pass.
- Choose cutoff frequency, resistance or capacitance as the unknown.
- Enter the two visible known quantities and their units.
- Optionally enter a test frequency to calculate gain and phase.
- Calculate and follow the input-based steps.
For low-pass: input → series resistor → output, with the capacitor from output to ground. For high-pass: input → series capacitor → output, with the resistor from output to ground. These output-node definitions are essential; swapping the measured component changes the response.
Unit selectors convert valid entered values, rather than reinterpreting the number. Hidden unknown fields are disabled and ignored. A blank optional test frequency omits the response calculation; it does not assume a signal frequency.
Optional capacitor assortments (paid link) should suit the actual voltage, polarity, dielectric and tolerance requirements of your circuit. The calculator does not select a physical part.
RC filter cutoff frequency, gain and phase formulas
Resistance: R = 1/(2πfcC)
Capacitance: C = 1/(2πfcR)
Let u = f/fc and τ = RC
Low-pass: |H| = 1/√(1 + u²), φ = −atan(u)
High-pass: |H| = u/√(1 + u²), φ = atan(1/u), for f > 0
Voltage gain in dB = 20 log10(|H|)
Use ohms, farads and hertz. The phase shown is in degrees and refers to output voltage relative to input voltage. At cutoff, both magnitude ratios are 1/√2 ≈ 0.7071068. This is about −3.010300 dB, commonly called the −3 dB point. The low-pass phase is −45°; the high-pass phase is +45°.
The decibel result describes a voltage ratio relative to unity. It is not a direct load-power calculation: the model has no output load or source impedance. For a single capacitor or inductor’s opposition at a frequency, use the Reactance Calculator.
RC filter examples: 1 kΩ and 100 nF
With R = 1 kΩ = 1,000 Ω and C = 100 nF = 0.0000001 F, τ = 0.0001 s = 100 µs. Cutoff is 1/(2π × 1,000 × 0.0000001) ≈ 1,591.549 Hz. This cutoff applies to either of the two output arrangements described above.
At 1 kHz, u ≈ 0.6283185. The low-pass voltage ratio is about 0.8467330, gain −1.445070 dB and phase −32.14191°. The high-pass ratio is about 0.5320180, gain −5.481473 dB and phase +57.85809°. The same R and C produce different responses because the output node differs.
To target 1 kHz with C = 100 nF, solve R = 1/(2π × 1,000 × 0.0000001) ≈ 1.591549 kΩ. This is a calculated ideal value, not a preferred resistor selection. The Resistor Color Code Calculator can help interpret markings on a chosen part.
Understand cutoff, attenuation and phase
Low-pass passes DC in the ideal model and progressively reduces higher-frequency voltage. High-pass has zero output at DC and approaches unity gain at high frequency. At DC its zero-amplitude output has no defined phase; +90° is the positive-frequency limiting phase, not a measurable DC output phase.
A first-order section approaches a 20 dB-per-decade attenuation slope far into its stopband. It is not a sharp frequency gate. Signals near cutoff are partly attenuated. Cascading two sections without buffering changes their loading, so multiplying independent unloaded responses does not generally describe the real cascade.
Optional digital oscilloscopes (paid link) can help compare nominal input/output magnitudes and phase using appropriate measurement conditions. The tool does not claim a waveform plot, active-filter design or measured performance. For a resistive output ratio instead, use the Voltage Divider Calculator.
Accuracy, source loading and RC filter limitations
Entered R must represent 0.001–1e12 Ω; C 1e−15–1,000 F; target cutoff 1e−9–1e12 Hz. Optional test frequency may be exactly zero, or 1e−9–1e12 Hz. All active values must be finite and nonnegative where explicitly allowed. Calculated inverse values may fall outside these entry ranges; they are mathematical values, not component recommendations.
This is one ideal unloaded RC section. Finite source resistance, output loading, capacitor ESR/leakage, tolerance, parasitics, layout and measurement probes can change cutoff, gain and phase. No RL, LC, RLC, active op-amp, band-pass, higher-order or PWM ripple/amplitude design is included. A timer pulse contains multiple frequency components; one sinusoidal test result does not reconstruct its complete waveform.
Results display seven significant digits while internal calculations use floating-point precision. Optional solderless breadboards (paid link) should be used only within the components’ and board’s ratings. For a distinct ideal inductor-capacitor frequency, use the LC Resonant Frequency Calculator.
RC Low-Pass & High-Pass Filter Calculator FAQs
For one ideal unloaded first-order RC section, fc = 1/(2πRC). Use resistance in ohms and capacitance in farads to get hertz.
With the same R and C under the same unloaded ideal assumptions, yes. Output across C is low-pass; output across R is high-pass. Gain and phase differ away from cutoff.
The voltage magnitude ratio is 1/√2, about 0.7071068 of the unity passband ratio. Its decibel value is about −3.010300 dB. This is not a direct load-power calculation.
Yes. Choose the unknown, enter the target cutoff and the other component, then calculate. The result is checked with the forward cutoff formula.
Ideal low-pass gain is one with zero phase. Ideal high-pass gain is zero and its DC output phase is undefined; +90° is only the positive-frequency limit.
No. It models an ideal zero-resistance source and no output load. Loading, parasitics and unbuffered cascades can change a real circuit’s response.
Sources and methodology
Independently implemented standard ideal-circuit equations, reviewed October 27, 2026. Linked organizations do not endorse this tool. The exact manufacturer datasheet governs real component limits.