Inductance Calculator
Calculate solenoid, toroid, air-core coil, required turns, stored energy, and AL-value inductance results with unit conversions and solution steps.
Calculator is for informational purposes only. Terms and Conditions
Choose what to calculate
Select the inductor method or design result you need.
Enter the known values
Only the fields needed for the selected calculation mode are shown.
Visual Check
Use the diagram to confirm the active geometry and key values.
Solution
Live result, quick checks, warnings, and full solution steps.
Quick checks
- Check—
Show solution steps See conversions, substitutions, assumptions, and result path
- Enter values to see the full calculation steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
Source and assumptions update based on the selected calculation mode.
- Assumptions will appear after a valid calculation.
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Calculator Guide
How to Use the Inductance Calculator
The Inductance Calculator above helps estimate coil, solenoid, toroid, air-core, AL-value, required-turns, and stored-energy results. Enter the known geometry, turns, permeability, AL value, current, or target inductance, then use the explanation below to understand the formula, units, assumptions, and whether the result is reasonable.
Inductance is the ability of a conductor or coil to store energy in a magnetic field and oppose changes in current. Most practical inductor values are expressed in millihenries, microhenries, or nanohenries, so unit selection is one of the most important parts of using the calculator correctly.
Quick Answer
To calculate inductance, choose the mode that matches your coil geometry, enter the known dimensions and turns, select the correct units, and review the result. For an ideal solenoid, the main relationship is \(L=\mu_0\mu_rN^2A/\ell\), which means inductance rises strongly with turns, coil area, and core permeability.
When not to rely on the simplified result
Do not use a simplified inductance estimate as the only basis for final magnetic component design. Real inductors are affected by saturation, DC bias, winding resistance, frequency, parasitic capacitance, temperature, core tolerance, and manufacturer-specific material data.
Inputs and Outputs Used by the Inductance Calculator
The calculator uses different inputs depending on the selected mode. A solenoid calculation needs turns, diameter, length, and permeability, while toroid, AL-value, required-turns, and energy modes use different known values.
| Mode | Typical Inputs | Main Output | Best Use |
|---|---|---|---|
| Solenoid / straight coil | Turns, coil diameter, coil length, relative permeability | Inductance | Basic coil or physics-style inductance estimate |
| Toroid | Turns, outer diameter, inner diameter, core height, relative permeability | Inductance | Approximate toroidal core calculations |
| Air-core coil | Turns, coil diameter, coil length | Inductance | Single-layer air-core winding and RF-style coil estimates |
| Required turns | Target inductance, diameter, length, relative permeability | Number of turns | Winding a coil to hit a target inductance |
| Stored energy | Known inductance and current | Energy in joules | Checking magnetic energy stored in an inductor |
| AL value | AL rating and turns | Inductance | Using manufacturer core data for ferrite or powdered iron cores |
Inductance Formula
The correct inductance formula depends on the coil geometry. Solenoids, toroids, air-core coils, target-turn calculations, stored energy, and AL-value calculations each use a different relationship.
In plain English, inductance usually gets larger when the coil has more turns, more magnetic area, or a stronger magnetic core, and it usually gets smaller when the magnetic path is longer.
Solenoid inductance
Use this for an ideal straight coil or solenoid where \(A\) is the coil cross-sectional area and \(\ell\) is the coil length.
Toroid inductance
For a toroid, \(A\) is the approximate core area and \(\ell_m\) is the mean magnetic path length around the core.
Air-core coil approximation
This Wheeler-style approximation uses \(r\) and \(\ell\) in inches and returns inductance in microhenries for a single-layer air-core coil.
Required turns
Use this rearranged solenoid formula when you know the target inductance and need to estimate the number of turns.
Stored energy and AL value
Stored energy uses inductance and current. AL-value calculations use a manufacturer-provided core factor and the number of turns.
What the Variables Mean
Every inductance formula should be used with consistent units. The most common base units are henries for inductance, meters for dimensions, amperes for current, and \(H/m\) for permeability.
\(L\)
Inductance, measured in henries. Practical coil values are commonly shown in \(mH\), \(\mu H\), or \(nH\).
\(N\)
Number of turns. Because many coil formulas use \(N^2\), small changes in turns can create large changes in inductance.
\(A\)
Cross-sectional area of the coil or core. For a circular solenoid, \(A=\pi r^2\).
\(\ell\) and \(\ell_m\)
\(\ell\) is coil length for a solenoid. \(\ell_m\) is mean magnetic path length for a toroid.
\(\mu_0\) and \(\mu_r\)
\(\mu_0=4\pi\times10^{-7}\,H/m\). \(\mu_r\) is relative permeability, with air close to 1.
\(A_L\), \(I\), and \(E\)
\(A_L\) is inductance per turns squared, \(I\) is current in amperes, and \(E\) is stored energy in joules.
How to Use the Calculator
Start by selecting the calculation mode that matches your known values. Then enter the coil dimensions, turns, permeability, target inductance, current, or AL value using the unit selectors shown in the calculator.
Which mode should I choose?
Use solenoid mode for straight coils, toroid mode for ring cores, air-core mode for single-layer coils without a magnetic core, required turns mode when you know the target inductance, stored energy mode when you know current, and AL value mode when you have manufacturer core data.
Select the calculation mode
Use solenoid for straight coils, toroid for ring cores, air-core for single-layer coils, required turns for target inductance, energy for \(E=\frac{1}{2}LI^2\), or AL value for manufacturer core ratings.
Enter known values
Enter measured or manufacturer-provided values when possible. Use average coil diameter, actual winding length, and a realistic core permeability or AL rating.
Check the units
Dimension errors are common. Verify whether the value is in millimeters, inches, meters, henries, millihenries, microhenries, or nanohenries.
Review the result and warnings
Use the result as an estimate, then check whether the value is physically reasonable for the coil size, turns, core material, and intended current or frequency.
How to Interpret Inductance Results
A low or high inductance value is not automatically good or bad. The right value depends on the circuit, frequency, current rating, core material, winding resistance, and how much energy or filtering the design requires.
There is no universally good inductance value. A good inductance is the value that gives the required impedance, filtering, energy storage, resonance, or current ripple behavior at the circuit’s operating current and frequency.
What to do with the result
Use the calculated inductance to compare coil designs, estimate required turns, choose a starting core, or check whether a measured value is in the expected range.
What changes the result most?
Turns often dominate because inductance scales with \(N^2\). Doubling turns ideally makes inductance about four times larger.
Sanity check
If a tiny air-core coil returns several henries, or a large magnetic core returns only a few nanohenries, recheck units, turns, and permeability.
What a suspicious result looks like
A suspicious inductance result is usually caused by entering diameter instead of radius, mixing inches and millimeters, using an unrealistic \(\mu_r\), entering \(mH\) as \(H\), or using an ideal solenoid formula for a short or irregular winding.
Input Checklist Before You Trust the Answer
Most inductance calculator errors are caused by geometry mistakes, unit mistakes, or assuming the core material behaves ideally. Check these items before using the result in a larger circuit calculation.
Confirm geometry
Use coil diameter for diameter fields, not radius. For toroids, confirm that the outer diameter is larger than the inner diameter.
Use realistic material data
Do not assume ferrite or powdered iron permeability is constant across frequency, temperature, and DC bias.
Check the turn count
Count complete turns consistently. In target-turn mode, round to a whole turn and check the resulting inductance error.
Separate estimate from final design
Use the calculator for sizing and comparison, then verify final coils by measurement and manufacturer data.
Worked Example
This example uses a common solenoid calculation because many users searching for an inductance calculator want to estimate coil inductance from turns and dimensions.
Formula
Area calculation
Substitution
Final answer
\(L\approx1.23\times10^{-4}\,H=0.123\,mH=123\,\mu H\). This is a reasonable order of magnitude for a small air-core solenoid with 100 turns.
Quick stored energy example
A \(10\,mH\) inductor carrying \(2\,A\) stores about \(0.02\,J\) of magnetic energy.
Quick AL value example
A core with \(A_L=100\,nH/turn^2\) and 20 turns has an estimated inductance of \(40\,\mu H\).
How to Visualize the Calculation
Inductance formulas connect geometry, turns, and magnetic material behavior. The diagram below keeps the labels simple so the important relationships are clear on desktop and mobile.
For a solenoid, the key inputs are \(N\), \(D\), \(\ell\), and \(\mu_r\). For a toroid, the key inputs are turns, core area, mean magnetic path length, and material data.
Turns
More turns usually increase inductance quickly because \(N\) is squared.
Area
A larger coil or core area increases the magnetic flux linkage.
Path length
A longer magnetic path generally reduces inductance for the same turns and core material.
Reference Checks
Inductance reference values depend heavily on geometry, core material, turns, current, and frequency. Instead of treating any range as universal, use these as rough scale checks.
| Range | Common Context | What to Check |
|---|---|---|
| nH to low µH | Small RF coils, traces, compact air-core windings | Lead length, parasitic capacitance, test frequency, and geometry |
| µH to mH | General inductors, filters, chokes, small wound coils | Core material, turns, saturation current, and winding resistance |
| mH to H | Larger chokes, relay coils, transformers, high-turn windings | Core saturation, copper resistance, heating, size, and voltage stress |
If the calculated value is far outside the expected scale for the physical size of the component, the first checks should be unit conversions, turn count, core permeability, and whether the selected formula matches the geometry.
Design Notes and Practical Ranges
Inductance is only one part of inductor design. A coil that has the desired inductance can still fail if it saturates, overheats, has too much resistance, or resonates at the operating frequency.
Target turns
Round calculated turns to a whole number, then recalculate actual inductance. A small rounding error may be acceptable for rough designs but not for tuned circuits.
Core limits
Ferrite and powdered iron materials have tolerance, frequency limits, loss behavior, and saturation behavior. Manufacturer datasheets matter.
Current limits
High current can reduce effective inductance through saturation and can increase heating through winding resistance.
Frequency limits
At higher frequencies, parasitic capacitance, skin effect, proximity effect, self-resonance, and Q factor can dominate performance.
Inductance Units and Conversions
The henry is the base SI unit of inductance, but practical inductors are often labeled in \(mH\), \(\mu H\), or \(nH\). Many wrong answers come from entering a microhenry value as millihenries or entering millimeters as meters.
Inductance conversions
For quick checks, \(1\,mH=1000\,\mu H\) and \(1\,\mu H=1000\,nH\). A value that is off by exactly 1000 often means the wrong inductance unit was selected.
Geometry conversions
Hidden unit trap
Air-core Wheeler formulas often use inches internally and return microhenries. Ideal solenoid formulas generally use meters and return henries. The calculator handles unit conversions, but manual checks must use the correct unit system.
Solenoid vs. Toroid vs. Air-Core vs. AL Value
The best calculation method is the one that matches the physical coil and the data you actually know. Do not force a solenoid formula onto a toroid or an AL-value core unless the assumptions make sense.
Use geometry formulas when
- You know the coil dimensions and number of turns.
- You need a learning estimate or first-pass design value.
- The winding is close to the ideal geometry assumed by the formula.
Use AL value when
- You have a core datasheet with a reliable \(A_L\) rating.
- You are winding on a ferrite or powdered iron core.
- You want a practical turns-to-inductance estimate from manufacturer data.
Common Mistakes
Inductance calculations are sensitive to units, geometry, and material assumptions. The same numbers can produce a dramatically different result if one value is entered in the wrong unit or interpreted incorrectly.
Do
- Use average coil diameter when the winding has thickness.
- Convert all dimensions consistently before checking the formula by hand.
- Use \(N^2\) carefully when comparing turn counts.
- Use manufacturer \(A_L\) data when it is available for a core.
- Measure the final coil when the circuit is sensitive to tolerance.
Don’t
- Do not enter radius in a diameter field.
- Do not treat relative permeability as fixed under all current and frequency conditions.
- Do not use a long-solenoid formula for every short or irregular coil.
- Do not ignore winding resistance, saturation current, or self-resonant frequency.
- Do not assume a calculated value exactly matches measured inductance.
Troubleshooting Unrealistic Results
If the answer looks too high, too low, or physically impossible, check the unit selectors and geometry first. Most inductance calculation problems are caused by scale errors or applying the wrong formula.
If your LCR meter reading does not match the calculator, check the test frequency, lead compensation, core bias, winding spacing, and whether the coil is near self-resonance. A simplified inductance formula usually estimates low-frequency inductance, while a real measurement depends on the test setup.
Result is too high
Check whether turns are too high, diameter was entered in meters instead of millimeters, or \(\mu_r\) is unrealistically large.
Result is too low
Check whether inductance was viewed in \(H\) instead of \(\mu H\), the coil length is too large, or the diameter was entered too small.
Toroid result fails
Confirm that the outer diameter is greater than the inner diameter and that the core height is positive.
Measured value is different
Check test frequency, fixture leads, winding spacing, core tolerance, DC bias, and whether the measurement instrument is zeroed correctly.
Assumptions and Limitations
The calculator is best used as an educational and preliminary engineering tool. It estimates inductance from simplified relationships and cannot fully model every real magnetic, thermal, and frequency-dependent effect.
Idealized geometry
Solenoid and toroid formulas assume simplified magnetic paths and uniform or approximate fields. Real windings may not match these assumptions.
Material behavior
Core permeability and AL value can vary with tolerance, air gap, temperature, DC bias, saturation, and frequency.
Frequency behavior
At high frequency, parasitic capacitance, Q factor, skin effect, proximity effect, and self-resonant frequency can matter more than the low-frequency inductance estimate.
Final verification
Final design should be verified with manufacturer data, measured inductance, saturation current, winding resistance, thermal limits, and applicable safety requirements.
Key Terms
These terms help connect the calculator inputs, formulas, and practical inductor behavior.
Inductance
A property that describes how strongly a conductor or coil opposes a change in current by storing energy in a magnetic field.
Relative permeability
A factor that describes how a material changes magnetic field behavior compared with air or vacuum.
AL value
A manufacturer-provided factor relating core inductance to turns squared, often given in \(nH/turn^2\).
Saturation
A condition where a magnetic core can no longer increase flux proportionally with current, reducing effective inductance.
Self-resonant frequency
The frequency where an inductor’s parasitic capacitance resonates with its inductance and changes the component behavior.
Magnetic path length
The approximate path followed by magnetic flux through a core, especially important in toroid calculations.
FAQ
How do you calculate inductance?
For an ideal solenoid, inductance is calculated with \(L=\mu_0\mu_rN^2A/\ell\), where \(N\) is turns, \(A\) is coil area, \(\ell\) is coil length, \(\mu_0\) is the permeability of free space, and \(\mu_r\) is relative permeability. Other coil shapes, such as toroids and air-core coils, use geometry-specific formulas.
Why does the number of turns affect inductance so much?
In many basic coil formulas, inductance is proportional to the square of the number of turns. Doubling the turns ideally increases inductance by about four times, assuming the geometry and core material stay the same.
What is AL value in an inductor?
AL value is a core factor that relates inductance to turns squared. It is commonly provided by magnetic core manufacturers and is often given in \(nH\) per turn squared. The basic relation is \(L=A_LN^2\).
Why is my measured inductance different from the calculator result?
Measured inductance can differ because real coils have winding spacing, lead length, core tolerance, air gaps, saturation, DC bias, parasitic capacitance, frequency-dependent permeability, and test instrument effects that simplified formulas do not fully model.
Can this inductance calculator be used for final inductor design?
Use the calculator for estimates, learning, comparison, and preliminary sizing. Final magnetic component design should be checked against manufacturer data, measured inductance, saturation current, winding resistance, thermal limits, frequency behavior, and applicable safety requirements.