# Inductor Calculator (X_L, Energy, Time Constant)

Calculate inductor properties: inductive reactance XL = 2 pi fL, stored energy E = 1/2 LI squared, and RL time constant tau = L/R. For circuit design and analysis.

## What this calculates

Inductors store energy in magnetic fields and resist changes in current. They are found in power supplies, filters, motors, and radio circuits. This calculator gives you the three most important inductor properties: reactance (how much it opposes AC current), stored energy, and the RL time constant that controls how fast current ramps up.

## Inputs

- **Inductance (L)** (mH) — min 0
- **Frequency (f)** (Hz) — min 0
- **Current (I)** (A) — min 0
- **Series Resistance (R)** (Ω) — min 0

## Outputs

- **Inductive Reactance (X_L)** (Ω) — Opposition to AC current at the given frequency
- **Impedance (Z) with Series R** (Ω) — Total impedance of the RL series circuit
- **Stored Energy** (J) — Energy stored in the magnetic field
- **Stored Energy** (mJ) — Stored energy in millijoules
- **Time Constant (τ)** (ms) — RL circuit time constant (L/R)
- **Voltage Across Inductor (AC)** (V) — V = I x X_L at the given frequency

## Details

## Key Inductor Formulas

### Inductive Reactance
**X_L = 2 pi f L**

Reactance is the inductor's opposition to alternating current. Unlike resistance, reactance increases with frequency. A 10 mH inductor has 6.28 ohms of reactance at 100 Hz but 62.8 ohms at 1 kHz. This frequency-dependent behavior is what makes inductors useful as filters.

### Stored Energy
**E = 1/2 L I squared**

An inductor carrying current stores energy in its magnetic field, just like a capacitor stores energy in its electric field. A 10 mH inductor carrying 5A stores 125 mJ. This energy gets released when the current is interrupted, which can create voltage spikes.

### RL Time Constant
**tau = L / R**

When you apply voltage to an RL circuit, the current does not jump instantly. It rises exponentially with time constant tau = L/R. After one time constant, current reaches 63.2% of its final value. After five time constants (5 tau), it is effectively at full value (99.3%).

### Impedance in an RL Circuit

When an inductor is in series with a resistor: **Z = sqrt(R squared + X_L squared)**

| Inductance | Frequency | X_L | With 100 ohm R: Z |
|-----------|-----------|-----|------------------|
| 10 mH | 100 Hz | 6.28 ohms | 100.2 ohms |
| 10 mH | 1 kHz | 62.8 ohms | 118.1 ohms |
| 10 mH | 10 kHz | 628 ohms | 636 ohms |

## Frequently Asked Questions

**Q: What is inductive reactance?**

A: Inductive reactance (X_L) is how much an inductor opposes alternating current, measured in ohms. Unlike resistance which dissipates energy as heat, reactance stores and returns energy. X_L = 2 pi f L, so it increases linearly with both frequency and inductance. At DC (f = 0), an ideal inductor has zero reactance and acts like a short circuit.

**Q: Why do inductors create voltage spikes when switched off?**

A: An inductor storing energy in its magnetic field (E = 1/2 LI squared) cannot change current instantaneously. When a switch opens, the inductor tries to maintain current flow by generating a large voltage spike. This is the same principle that makes ignition coils in cars work -- they step up 12V to thousands of volts. In circuits, a flyback diode protects against these spikes.

**Q: What is the difference between inductance and reactance?**

A: Inductance (L, measured in Henries) is a physical property of the coil -- it depends on the number of turns, core material, and geometry. Reactance (X_L, measured in ohms) is the resulting opposition to AC current at a specific frequency. Think of inductance as the component's inherent property and reactance as its behavior at a given frequency.

**Q: How does the RL time constant work?**

A: The time constant tau = L/R determines how fast current rises in an RL circuit. A 10 mH inductor with a 100 ohm resistor has tau = 0.1 ms. After 0.1 ms the current reaches 63% of its final value, after 0.5 ms it reaches 99.3%. Larger inductance or smaller resistance means slower rise time. This is useful in motor drivers, relay circuits, and power converters.

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Source: https://vastcalc.com/calculators/physics/inductor
Category: Physics
Last updated: 2026-04-08