What this calculator does
Impedance is the total opposition a circuit presents to alternating current, combining plain resistance with reactance, the frequency-dependent opposition from capacitors and inductors. Because resistance and reactance act at right angles to each other in the maths, they cannot simply be added: the combined impedance is Z = square root of (R squared plus X squared), the same shape as finding the hypotenuse of a right triangle.
This impedance calculator handles the two most common single-component cases: a resistor in series with a capacitor, and a resistor in series with an inductor. Enter the resistance, the frequency of the AC signal, and either the capacitance or inductance, and it works out the reactance first, then combines it with the resistance to give the overall impedance and the phase angle between voltage and current.
The formula
For a series RC circuit, the capacitor contributes capacitive reactance Xc = 1 / (2πfC), which falls as frequency rises. For a series RL circuit, the inductor contributes inductive reactance XL = 2πfL, which rises with frequency. Either way, the combined impedance is Z = √(R² + X²), and the phase angle between voltage and current is the arctangent of X divided by R. Current lags voltage in an RL circuit and leads it in an RC circuit.
| Term | Meaning |
|---|---|
| Z | Impedance, the combined AC opposition, in ohms. |
| R | Resistance, in ohms. |
| Xc, XL | Capacitive or inductive reactance, in ohms. |
| f | Frequency of the AC signal, in hertz. |
The inputs explained
| Field | What to enter |
|---|---|
| Circuit type | Choose whether the reactive component is a capacitor (series RC) or an inductor (series RL). |
| Resistance (R) (Ω) | The resistance in the circuit. |
| Frequency (f) (Hz) | The frequency of the AC signal driving the circuit. |
| Capacitance (C, for RC) (µF) | The capacitor value, used only for the RC case. |
| Inductance (L, for RL) (mH) | The inductor value, used only for the RL case. |
When to use it
Sizing a filter or crossover network
Audio crossovers and simple filters combine a resistor with a capacitor or inductor, and the overall impedance the source sees at a given frequency affects how much power actually reaches the load.
Checking a decoupling or coupling capacitor
A coupling capacitor in series with a signal path adds reactance that only becomes negligible well above some frequency, so combining it with the circuit resistance shows where that point actually is.
Estimating current draw in an AC circuit
Once impedance is known, current follows directly from voltage divided by impedance, the AC equivalent of Ohm's law, useful for checking that a component is not overloaded at the operating frequency.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How impedance changes with frequency for a fixed RC circuit
The same resistor and capacitor, checked across a range of frequencies.
| Frequency | Impedance (Z) | Capacitive reactance (Xc) |
|---|---|---|
| 100 Hz | 1,594.688 Ω | 1,591.549 Ω |
| 500 Hz | 333.648 Ω | 318.310 Ω |
| 1,000 Hz | 187.964 Ω | 159.155 Ω |
| 5,000 Hz | 104.944 Ω | 31.831 Ω |
| 10,000 Hz | 101.259 Ω | 15.915 Ω |
Questions
Why can't I just add resistance and reactance directly?
Resistance dissipates energy as heat while reactance stores and returns it, and the two effects are 90 degrees out of phase with each other. Combining them with Pythagoras' formula, Z = √(R² + X²), correctly accounts for that phase difference rather than overstating the total opposition.
What is the difference between this and a capacitive reactance calculator?
A capacitive reactance calculator gives Xc alone, the opposition from the capacitor by itself. This calculator takes that reactance and combines it with a resistor's resistance to give the impedance of the whole series circuit, which is what actually limits current in practice. See the capacitive reactance calculator for the reactance-only version.
What does the phase angle tell me?
It is the angle by which voltage leads or lags current in the circuit. In a series RC circuit current leads voltage, and in a series RL circuit current lags voltage. A phase angle near zero means the circuit behaves mostly like a plain resistor; near 90 degrees means reactance dominates.
Does this handle circuits with both a capacitor and an inductor?
No, this covers the two simple single-reactance cases, resistor with capacitor or resistor with inductor. A circuit with all three components requires combining capacitive and inductive reactance first (they partially cancel, since they act in opposite directions) before applying the same Z = √(R² + X²) formula.
For the capacitive reactance figure on its own, see the capacitive reactance calculator. For an RC filter's cutoff frequency rather than its impedance, see the high pass filter calculator.