Calculate Inductance

Calculator and formulas for calculating the inductance of coils

Inductance Calculator

Inductance and Coils

This function calculates the relationship between inductance, voltage, current and time. To calculate, select with the radio buttons which value should be calculated. Then enter the required values and click the 'Calculate' button.

Results
Inductance:
Current:
Voltage:
Time:

Inductance

What is Inductance?

Inductance is the property of electrical circuits to oppose a change in electrical current through self-induction. It is measured in Henry (H) and is particularly important for coils and transformers.

Basic Formula
\[L = \frac{U \cdot t}{I}\]

Inductance from voltage, time and current.

Formula Variations
\[U = \frac{L \cdot I}{t}\]
\[I = \frac{U \cdot t}{L}\]
\[t = \frac{I \cdot L}{U}\]

Calculation of other quantities with given inductance.

Example Calculations

Practical Calculation Examples

Example 1: Calculate Inductance

Given: U = 12 V, I = 2 A, t = 0.5 s

\(L = \frac{U \cdot t}{I} = \frac{12 \text{ V} \cdot 0.5 \text{ s}}{2 \text{ A}}\)
\(L = 3 \text{ H}\)
Example 2: Calculate Current

Given: L = 10 mH, U = 5 V, t = 2 ms

\(I = \frac{U \cdot t}{L} = \frac{5 \text{ V} \cdot 0.002 \text{ s}}{0.01 \text{ H}}\)
\(I = 1 \text{ A}\)
Example 3: Calculate Voltage

Given: L = 50 µH, I = 100 mA, t = 10 µs

\(U = \frac{L \cdot I}{t} = \frac{50 \times 10^{-6} \text{ H} \cdot 0.1 \text{ A}}{10 \times 10^{-6} \text{ s}}\)
\(U = 0.5 \text{ V}\)
Important Conversions
Inductance Units:
1 H = 1,000 mH
1 mH = 1,000 µH
1 µH = 1,000 nH
1 nH = 0.001 µH
Current Units:
1 A = 1,000 mA
1 mA = 1,000 µA
1 kA = 1,000 A
1 µA = 0.001 mA

Inductance - Theory and Formulas

What is Inductance?

Inductance is a property of circuits or components, especially coils. Self-inductance results from the rate of change of electric current and voltage over a period of time. It describes the relationship between the induced voltage and the current change.

Calculation Formulas

Inductance
\[L = \frac{U \cdot t}{I}\]

Inductance from voltage, time and current.

Voltage
\[U = \frac{L \cdot I}{t}\]

Self-induced voltage with current change.

Current
\[I = \frac{U \cdot t}{L}\]

Current from voltage, time and inductance.

Time
\[t = \frac{I \cdot L}{U}\]

Time for a specific current change.

Properties of Inductors

Behavior with Current Change
  • Lenz's Law: Induced voltage opposes current change
  • Self-induction: Coil induces voltage when current changes
  • Energy storage: Magnetic field stores energy
  • Time constant: τ = L/R determines rise time
Construction Types
  • Air coils: No magnetic losses
  • Iron core coils: Higher inductance
  • Ferrite core coils: HF-suitable
  • Toroidal coils: Low stray field

Practical Applications

Filters:
• Low-pass filters
• High-pass filters
• EMI filters
• Crossover networks
Energy Storage:
• Switching regulators
• DC/DC converters
• Flyback converters
• Storage chokes
Transformers:
• Power transformers
• Audio transformers
• Pulse transformers
• Current transformers

Inductance Calculation for Coils

Coil Parameters
Air Core Coil (Cylinder):
\[L = \frac{\mu_0 \cdot N^2 \cdot A}{l}\]

N = Number of turns, A = Cross-sectional area, l = Length

Coil with Core:
\[L = \frac{\mu_0 \cdot \mu_r \cdot N^2 \cdot A}{l}\]

μr = Relative permeability of core material

Design Guidelines

Important Design Aspects
  • Core material: Iron powder for high currents, ferrite for HF
  • Winding type: Layered or random for different characteristics
  • Saturation: Core material limits maximum current
  • Losses: Copper losses (I²R) and core losses (f²)
  • Self-resonance: Parasitic capacitance limits frequency range
  • Temperature: Winding resistance increases with temperature

Mathematical Relationships

Energy in Magnetic Field
\[W = \frac{1}{2} L I^2\]

Stored magnetic energy

Reactance
\[X_L = 2\pi f L = \omega L\]

Inductive reactance with AC current

Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?


Other induction calculators

Inductance  •  Reactance of a coil  •  Cutoff frequency R/L  •  Differentiator R/L  •  Highpass filter R/L  •  Lowpass filter R/L  •  Series circuit R/L  •  Parallel circuit R/L  •  Transformer  •