RC High-Pass Calculator
Find the cutoff of a first-order RC high-pass and the gain, attenuation, and phase at the frequency you type.
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Result
About this tool
The page treats the circuit as one series capacitor and one resistor to ground, the ordinary first-order high-pass. You type a resistance, a capacitance, and a test frequency. Each number is multiplied by the unit selected beside it. The defaults are 10, kilohms, 100, nanofarads, and 1000 hertz, so the values that actually enter the formula are 10000 ohms, 1e-7 farads, and 1000 hertz. Any of those three that is not strictly positive stops the report with the positive-values error. There is no inductor, no second pole, and no load resistance in this calculation.
Cutoff frequency is 1 / (2πRC). With the defaults that is 1 / (2π × 10000 × 1e-7) = 159.1549430919 Hz, and the report prints it with the engineering formatter. The time constant τ is R times C, which is 0.001 seconds and prints as 1 ms. Capacitive reactance at the test frequency is 1 / (2πfC). At 1000 Hz and 100 nF that is 1.591549430919 kΩ. High-pass gain is the ratio f/fc divided by the square root of 1 plus that ratio squared. At 1000 Hz the ratio is about 6.283, and the gain prints as 0.9876. Attenuation is 20 log10 of that gain, which prints as -0.11 dB. Phase is 90 degrees minus the arctangent of f/fc, in degrees, which prints as 9.04°.
At the cutoff itself the ratio is 1, so the gain is 1/sqrt(2), which prints as 0.7071, and the phase is 45.00°. That is the usual −3 dB point: 20 log10(0.7071) is about −3.01 dB, though the page will show the two-decimal attenuation for whatever test frequency you typed, not a separate −3 dB annotation. Well below the cutoff the gain falls toward 0 and the phase rises toward 90°. Well above it the gain sits near 1 and the phase sits near 0°. The gain line is a voltage ratio, printed with four digits after the decimal and an x. It is not a power gain. The formulas are ideal lumped elements. They ignore capacitor ESR, resistor tolerance, op-amp limits, and the source resistance of whatever is driving the filter. The unit menus are the whole set of prefixes: ohms, kilohms, megohms; picofarads, nanofarads, microfarads, millifarads; hertz, kilohertz, megahertz. The page does not pick a preferred E24 pair for you. That search lives on the separate preferred-RC designer. Changing the test frequency does not move the cutoff. It only moves the gain, the attenuation, the phase, and the reactance.
Example. 10 kΩ and 100 nF, tested at 1000 Hz, report a cutoff of 159.1549430919 Hz, a time constant of 1 ms, reactance of 1.591549430919 kΩ, gain 0.9876x, attenuation -0.11 dB, and phase 9.04°.
Limit. Resistance, capacitance, and test frequency must all be strictly positive. The model is one series capacitor into a resistor to ground, with no load and no second pole.
What cutoff does 10 kΩ and 100 nF give?
Those are the default fields: 10000 ohms and 100 nanofarads. Cutoff is 1/(2πRC) = 159.1549430919 Hz. The time constant RC is 1 ms. At a test frequency of 1000 Hz the high-pass gain prints as 0.9876x, the attenuation as -0.11 dB, and the phase as 9.04°.
What is the gain at the cutoff?
When the test frequency equals the cutoff, the ratio f/fc is 1 and the gain is 1/sqrt(2), printed as 0.7071x. The phase formula (π/2 − atan(f/fc)) in degrees is then 45.00°. Attenuation is 20 times log10 of the gain, so that point is about −3 dB.
Does this include the load or a second stage?
No. The transfer function is the ideal first-order high-pass of a series capacitor and a shunt resistor. Source impedance, capacitor ESR, and a following stage are not in the arithmetic. Non-positive R, C, or test frequency is rejected.
Which units does the form multiply by?
The resistance menu is ×1, ×1000, or ×1000000. The capacitance menu is picofarads, nanofarads, microfarads, or millifarads. The frequency menu is hertz, kilohertz, or megahertz. The number you type is multiplied by the selected factor before the formula runs.