# [Maxwell Bridge Calculator](https://blog.hirnschall.net/tools/maxwell-bridge/) author: [Sebastian Hirnschall](https://blog.hirnschall.net/about/) meta description: Calculate unknown inductance and series resistance from a balanced Maxwell-Wien bridge. Enter R2, R3, R4, C4 at null; L_x, R_x, and Q are computed. meta title: Maxwell Bridge Calculator — Inductance and Series Resistance date published: 11.05.2026 (DD.MM.YYYY format) date last modified: 11.05.2026 (DD.MM.YYYY format) --- Calculator ---------- Enter the four bridge components at balance. The unknown inductance \( L\_x \) and its series resistance \( R\_x \) are calculated from the balance conditions. Providing the test frequency also yields the quality factor \( Q \). * R2 (ratio arm): * Ω kΩ MΩ * R3 (ratio arm): * Ω kΩ MΩ * R4 (standard arm, variable): * Ω kΩ MΩ * C4 (standard arm, parallel with R4): * µF nF pF --- * Test frequency (f) — optional: * Hz kHz Enter all four bridge components to calculate. Calculate Maxwell Bridge — Explanation ---------------------------- The Maxwell bridge (more precisely the Maxwell-Wien bridge) is an AC bridge circuit used to measure the inductance and series resistance of an unknown inductor. It places the unknown inductor \( L\_x \) with its winding resistance \( R\_x \) in one arm, balances it against a known capacitor in an adjacent arm, and reads off \( L\_x \) and \( R\_x \) directly from the values of the calibrated components at null. The bridge has four arms. The unknown arm contains \( L\_x \) in series with \( R\_x \). The opposite arm (the standard arm) contains a known resistor \( R\_4 \) in parallel with a known capacitor \( C\_4 \). The two remaining arms are plain resistors \( R\_2 \) and \( R\_3 \). An AC source drives one diagonal and a null detector (galvanometer or oscilloscope) monitors the other. Balance Conditions ------------------ At balance, no current flows through the detector. Setting the complex impedance products of opposite arm pairs equal and separating real and imaginary parts gives two independent equations: \[ L\_x = R\_2 \cdot R\_3 \cdot C\_4 \] \[ R\_x = \frac{R\_2 \cdot R\_3}{R\_4} \] These two conditions are independent of frequency, which is one of the key practical advantages of the Maxwell bridge: the source frequency does not need to be known precisely. The ratio arms \( R\_2 \) and \( R\_3 \) always appear as a product, so only their product \( R\_2 R\_3 \) matters — in practice one is often kept fixed while the other is adjusted in decade steps to set the range. The quality factor of the measured inductor at the test frequency \( f \) is: \[ Q = \frac{\omega L\_x}{R\_x} = \omega C\_4 R\_4 \] where \( \omega = 2\pi f \). \( Q \) can be read directly from the standard arm components once the bridge is balanced. Valid Q Range ------------- The Maxwell bridge works well for medium-Q inductors, typically in the range \( 1 \leq Q \leq 10 \). Outside this range, balance becomes difficult to achieve because the real and imaginary balance conditions become nearly dependent, making the null hard to locate. For high-Q inductors (\( Q > 10 \)) the Hay bridge is the better choice: it uses a capacitor in series rather than parallel with \( R\_4 \), which suits high-Q measurements naturally. The calculator outputs a warning when the computed Q falls outside the useful range. Purpose of the Calculator ------------------------- In a physical measurement, the bridge is brought to null by adjusting the variable components (typically \( R\_4 \) for the resistive balance and \( R\_3 \) or \( C\_4 \) for the reactive balance). Once the detector reads zero, the component values at that point are entered here to recover \( L\_x \) and \( R\_x \). No frequency measurement is needed for \( L\_x \) and \( R\_x \); frequency is only required if Q is also wanted. The formulas can also be rearranged for component selection when designing a bridge for a target inductance range. Fixing \( C\_4 \) and choosing \( R\_2 R\_3 = L\_x / C\_4 \) sets the inductance scale, and choosing \( R\_4 = R\_2 R\_3 / R\_x \) sets the resistance scale. Related Tools ------------- * [Schering Bridge Calculator](https://blog.hirnschall.net/tools/schering-bridge/) — the capacitive equivalent: measures unknown capacitance and dissipation factor. * [Wheatstone Bridge Calculator](https://blog.hirnschall.net/tools/wheatstone-bridge/) — DC bridge for measuring unknown resistance. * [Inductor Impedance Calculator](https://blog.hirnschall.net/tools/inductor-impedance/) — compute \( X\_L \) and \( |Z| \) from the measured \( L\_x \) and \( R\_x \). * [Inductor Energy Calculator](https://blog.hirnschall.net/tools/inductor-stored-energy/) — compute the energy stored in the measured inductor at a given current. More calculators: [blog.hirnschall.net/tools/](https://blog.hirnschall.net/tools/).