Please enter all required numeric values.
RESULTS
Input Parameters Specification
Wire Diameter dDiameter of the round wire used to form the loop.
Loop Diameter DMain circular loop diameter measured across the loop center.
Relative Permeability μrUse 1 for air or normal non-magnetic material.
OutputCalculated loop inductance in henries.
Practical Operational Examples
RF Loop Design
Estimate inductance of circular wire loops for antennas and RF circuits.
Coil Prototype
Change loop diameter or wire diameter to see how inductance changes.
Diagrams & Theory
A circular wire loop inductance depends on the main loop diameter, the wire thickness, and the magnetic permeability of the surrounding material.
Formulas & Mathematical Logic
L = μ0 × μr × (D / 2) × [ ln(8D / d) - 2 ]
μ0 = 4 × π × 10^-7 H/m
D = loop diameter, d = wire diameter, μr = relative permeability.
The calculator converts wire diameter and loop diameter into meters first, then applies the circular loop inductance formula.
Step-by-Step Example
Example: Wire diameter d = 1 mm, loop diameter D = 50 mm, relative permeability μr = 1.
Convert units: d = 0.001 m and D = 0.05 m.
Loop radius term used by the formula is D / 2 = 0.025 m.
The logarithmic part becomes ln(8D / d) - 2.
The final value is displayed in scientific notation as henries.
How to Use This Calculator
Enter the diameter of the wire used to make the loop.
Select the correct unit for wire diameter.
Enter the main loop diameter measured across the circular loop.
Enter relative permeability. Use 1 for air, copper wire, and normal non-magnetic surroundings.
Click Calculate to estimate the loop inductance.
About This Calculator
Estimate inductance of a single circular wire loop.
The CalcBoy Wire Loop Inductance Calculator helps estimate inductance from loop diameter, wire diameter, and magnetic permeability.
A circular wire loop stores magnetic energy when current flows through it. The loop diameter controls the size of the magnetic field path, while wire diameter affects the logarithmic part of the inductance expression. In practice, a larger loop generally increases inductance, while a thicker conductor tends to reduce the calculated value slightly for the same loop size.
This calculator is useful for RF loop experiments, single-turn loop antennas, magnetic pickup loops, pulse-current paths, sensing coils, and quick prototype checks. It is especially handy when you want a first-pass estimate before building the loop or testing it with an LCR meter. For high-frequency antenna work, the physical environment, nearby metal objects, solder joints, and lead shape can all shift the measured value, so the calculated result should be treated as a practical engineering estimate.
Best UseSingle circular loop, RF loop, sensor loop, or prototype coil estimate.
Loop DiameterBigger loop diameter increases magnetic field area and usually raises inductance.
Wire DiameterThicker wire changes the logarithmic correction and can reduce estimated inductance.
Design ReminderLead length, nearby metal, and mounting style can change the real measured value.
Tip: For loop antennas or RF pickup loops, calculate the inductance first, then verify the final built loop with an LCR meter because bending, solder pads, and connector leads can add extra inductance.
Frequently Asked Questions
What is wire loop inductance?
Wire loop inductance is the inductance produced by a current flowing around a circular conductor loop. It depends on loop size, wire thickness, and magnetic permeability.
What value should I use for relative permeability?
Use μr = 1 for air, copper wire, and most normal non-magnetic materials around the loop.
Does a larger loop diameter increase inductance?
Yes. A larger loop usually stores more magnetic field energy and increases inductance.
Does thicker wire reduce inductance?
For the same loop diameter, thicker wire generally reduces the calculated inductance slightly because the wire diameter appears inside the logarithmic term.
Can this calculator be used for loop antennas?
Yes, it is useful for first-pass RF loop antenna estimates, but final tuning should be checked with real measurement.
Is this formula exact for all loop shapes?
No. It is meant for a circular wire loop. Square loops, rectangular loops, and PCB loops need different geometry formulas.
Why is the result shown in scientific notation?
Small inductance values are often tiny fractions of a henry, so scientific notation keeps the output compact and readable.
Related Calculators
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Coil Inductance CalculatorCalculate single, multi-layer, and flat spiral coil inductance.
Inductance Reactance CalculatorConvert inductance into reactance at a selected frequency.