Helical Coil Calculator

Wheeler's formula estimates the inductance of a single-layer air-core coil.

How the Math Works

The Helical Coil Calculator uses Wheeler's formula to estimate the inductance of an air-core coil: L(µH) = d²·n² ÷ (18d + 40l). Here, d is the coil diameter in inches, n is the number of turns, and l is the coil length in inches. The formula approximates inductance by balancing geometric factors: the square of the diameter and turns dominate the numerator, while the denominator accounts for the coil's physical proportions. This empirical model assumes no magnetic core, making it ideal for estimating inductance in simple cylindrical coils used in electronics.

Practical Applications

Engineers and hobbyists use this calculator to design inductors for radio frequency (RF) circuits, filters, and oscillators. By inputting coil dimensions, users can verify if their physical design will achieve the desired inductance without expensive prototyping. It's particularly useful for tuning circuits in transmitters, wireless chargers, or audio equipment, where precise inductance values ensure optimal signal performance. The formula also aids in troubleshooting by allowing users to estimate inductance from an existing coil's measurements when specifications are unknown.

Day-to-Day Use

Air-core inductors calculated using this method are integral to modern electronics, from smartphones and Wi-Fi routers to medical devices and electric vehicles. Understanding coil inductance helps improve device efficiency and signal clarity in everyday gadgets. For example, knowing the inductance of a coil in a wireless charging pad ensures it transfers power effectively to your phone. Even in DIY projects like building a radio or drone controller, this calculator provides quick estimates to guide component selection, making advanced electronics more accessible to enthusiasts and professionals alike.

Worked example

20 mm dia, 30 mm long, 30 turns → about 4.5 µH.

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