RC low pass filter

Calculator and formulas for calculating the parameters of an RC low pass

RC low pass online calculator

This function calculates the properties of a low-pass filter consisting of a resistor and a capacitor. The output voltage, attenuation and phase rotation are calculated for the given frequency.

RC low pass calculator

Input voltage
Decimal places
Reactance XC
Output voltage U2
Attenuation dB
Phase shift φ
Cutoff frequency
Impedance Z
Voltage UR
Current I
Current I
Time constant τ


\(\displaystyle C\) = Capacity [F]

\(\displaystyle R\) = Resistance [Ω]

\(\displaystyle U_1\) = Input voltage [V]

\(\displaystyle U_2\) = Output voltage [V]

\(\displaystyle X_C\) = Capacitive reactance [Ω]

\(\displaystyle φ\) = Phase angle [°]

\(\displaystyle Z\) = Input impedance [Ω]

\(\displaystyle I\) = Current [A]

\(\displaystyle U_R\) = Voltage at the restistor [V]

Formulas for the RC low pass filter

Calculate the voltage ratio

The output voltage U2 of an RC low pass is calculated according to the following formula.

\(\displaystyle U_2=U_1 ·\frac{1} {\sqrt{1 + (2 · π · f · R · C)^2}}\)

or easier if XC is known

\(\displaystyle U_2=U_1 ·\frac{X_C}{\sqrt{R^2 + X_C^2}}\)
\(\displaystyle X_C=\frac{1}{2 π · f ·C}\)

Attenuation in decibels

At the resonance frequency, the damping is 3 dB. If the input and output voltage are known, the attenuation for all frequencies can easily be calculated using the following formula.

\(\displaystyle V_u=20 · lg \left(\frac{U_2}{U_1} \right) \)

If the voltages are not known, the following formula is used.

\(\displaystyle V_u=20·lg\left(\frac{1} {\sqrt{1 + (2 · π · f · R · C)^2}}\right)\)

or simply shown

\(\displaystyle V_u=20·lg\left(\frac{1} {\sqrt{1 + (ω · R · C)^2}}\right)\)

Phase shift

In an RC low pass, the output voltage lags the input voltage by 0 ° - 90 °, depending on the frequency. At the resonance frequency, the phase shift is -45 °. At low frequencies, it tends to 0. At high frequencies, the phase shift in the direction of -90 °. The phase shift can be calculated using the following formula.

\(\displaystyle φ=acos \left(\frac{U_2}{U_1} \right))\)
\(\displaystyle φ= arctan (ω · R ·C)\)

Cutoff frequency

At the limit frequency fg bzw. ωg the value of the amplitude-frequency response (ie the magnitude of the transfer function) is 0.707. This corresponds to -3 dB.

\(\displaystyle 0.707= \frac{1}{\sqrt{2}}\)

Cutoff frequency formulas

\(\displaystyle ω_g= \frac{1}{R ·C} ⇒\)
\(\displaystyle f_g=\frac{1}{2·π·R·C}\)

\(\displaystyle R=\frac{1}{2·π·f_g·C}\)
\(\displaystyle C=\frac{1}{2·π·f_g·R}\)


\(\displaystyle Z=\sqrt{X_C^2 + R^2} \)


\(\displaystyle I=\frac{U}{Z} \)

Restistor voltage

\(\displaystyle U_R=R ·I \)

Time constant

\(\displaystyle τ=C ·R \)

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