RC Low-Pass Filter Gain Calculator

How it is calculated

Enter resistance R in ohms, capacitance C in farads (1 µF = 0.000001, 100 nF = 0.0000001) and frequency f in hertz. The tool computes x = 2π × f × R × C, then the voltage gain gain = 1 ÷ √(1 + x²) (output voltage divided by input voltage, unloaded) and dB = 20 × log₁₀(gain). R and C must be above zero and f cannot be negative; at f = 0 the gain is exactly 1.00 (0.00 dB). Gain is rounded to two decimals, so very small values show as 0.00 even though the dB figure is still meaningful. It gives magnitude only, with no phase shift, and assumes the filter drives no load.

Common mistakes

• Typing capacitance in microfarads or nanofarads. The field is farads, so 100 nF must be entered as 0.0000001; typing 100 gives a huge capacitor and almost no gain.
• Entering the frequency in kHz. The field is in hertz, so 1 kHz is 1000.
• Confusing gain with power ratio. The dB value here is for voltage, 20·log₁₀, so halving the voltage is about −6 dB, not −3 dB.
• Expecting −3 dB at any frequency. The −3 dB point (gain 0.71) occurs only at the cutoff frequency 1 ÷ (2π × R × C).
• Ignoring the load. The formula assumes an unloaded output, so a low-impedance load after the filter will change the real response.