| Inductive/Capacitive Reactance Equations |
An Alternating Current is one whose amplitude of current flow periodically rises from zero to a maximum in one direction, decreases to zero, changes its direction, rises to a maximum in the opposite direction, and decreases to zero again. This complete process, starting from zero, passing through two maximums in opposite directions, and returning to zero again, is called a cycle. The number of times per second that a current passes through the complete cycle is called the frequency of the current and is specified in Hertz. One cycle is equivalent to one hertz.
When a changing current flows through a inductor a counter-electromotive force is developed, opposing any change in the initial current. This property of an inductor causes it to offer opposition to a change in current. The measure of opposition offered by an inductor to an alternating current of a given frequency is known as its Inductive Reactance (XL). The formula for inductive reactance, in terms of Inductance (L) and Frequency (F), is listed on the right.
Capacitors have a similar property although in this case the opposition is to any change in the voltage across the capacitor. This property is called Capacitive Reactance (XC) and is calculated as shown in the image on the right, in terms of Capacitance (C) and Frequency (F).
The graph is a visual example of Inductive/Capacitive Reactance, for two specific component values, across two decades of frequency. The horizontal scale is Frequency in Hertz and the vertical scale is Reactance, in Ohms. A 0.002 uF Capacitor and a 1.26 mH Inductor. Note that, as frequency increases, Capacitive Reactance (XC) decreases and Inductive Reactance (XL) increases. While the Inductive and Capacitive Reactance equations are linear, using a logarithmic scale for frequency make things easier to see over large spans.
Note the very center of the graph (100KHz). At that point the Inductive/Capacitive Reactances are equal. This point is known as Resonance.
| Calculators |
Below are a group of calculators for working with Inductors and Capacitors in tuned circuits. Each of the calculators shows the equation being used.
- Two of the calculators determine Reactance at specific Frequencies, for specified Inductors and Capacitors.
- One calculates Resonant Frequency, for any combination of Inductor and Capacitor.
- One calculates Q at, a specific Frequency, for Inductors, given Inductance and Resistance.
- And finally, two calculators allow the calculation of Inductance, given Fequency and Capacitance or the calculation of Capacitance, given Frequency and Inductance.
In all of the calculators, enter your values and select your dimension. Then click anywhere outside the calculator and the Reactance will be calculated and displayed.
Inductive and Capacitive Reactance Calculators
| Inductive Reactance Calculator | |
|---|---|
| Inductance (L) (mH, uH, nH) |
Frequency (F) (MHz, KHz, or Hz) |
|
XL = 2 x Π x F x L |
|
| Reactance (XL) = 791.7 Ω | |
| Capacitive Reactance Calculator | |
|---|---|
| Capacitance (C) (F, mF, uF, nF, pF) |
Frequency (F) (MHz, KHz, or Hz) |
|
XC = 1 2 x Π x F x C |
|
| Reactance (XC) = 795.8 Ω | |
For the equation on the left, L the Inductance of the coil in Henrys, F is the frequency in Hertz, and XL is the Inductive Reactance in Ohms
For the equation on the right, C is the Capacitance of the capacitor in Farads, F is the frequency in Hertz, and XC is the Capacitive Reactance in Ohms
Tuned Circuit Frequency and Inductor Q Calculator
| Tuned Circuit Frequency Calculator | |
|---|---|
| Inductance (L) (H, mH, uH, nH) |
Capacitance (C) (F, mF, uF, nF, pF) |
|
F = 1 2 x Π L x C |
|
| Frequency (F) = 100.3 KHz | |
| Inductor Q Calculator | |
|---|---|
| Inductance (L) (mH, uH, nH) |
Frequency (F) (MHz, KHz, or Hz) |
| Resistance (r) (Ω, KΩ, or MΩ) |
Q = 2 × PI × F × L r |
As an inductor is made from a coil of wire it will always contain resistance. The Quality factor, or Q factor is the ratio of energy stored in a coil to the energy lost during one cycle. The energy losses are due to internal resistance of the coil and absorption of the magnetic field. Coils made with thick wire will have less resistance and higher Q than a coil made with a smaller diameter wire. A high Q parallel tuned circuit will have a narrow bandwidth at resonance and low Q circuits will have wider bandwidths.
In the equation r is coil internal resistance in Ohms, F is frequency in Hertz and L inductance of coil in Henries.
Calculate Inductance or Capacitance from Frequency
| Calculate C from L/F | |
|---|---|
| Frequency (F) (MHz, KHz, or Hz) |
Inductance (L) (H, mH, uH, nH) |
|
C = 1 ( 2 x Π x F )2 x L |
|
| Capacitance (C) = 2010 pF | |
| Calculate L from C/F | |
|---|---|
| Frequency (F) (MHz, KHz, or Hz) |
Capacitance (C) (F, mF, uF, nF, pF) |
|
L = 1 ( 2 x Π x F )2 x C |
|
| Inductance (L) = 1.3 mH | |
If you have a Frequency and Inductance value, and want to calculate a Capacitance value, for a tuned circuit, use the calculator on the left.
If you have a Frequency and Capacitance value, and want to calculate a Inductance value, for a tuned circuit, use the calculator on the right.