Physical Coil Properties Calculator – Wire Length and Resistance

Coil Geometry and Material Properties Estimator

Physical Coil Formulas

Formula

$$l = N \cdot \pi \cdot D$$ $$R = \rho \cdot \frac{l}{A}$$ $$m = l \cdot \gamma$$ $$n = \frac{N}{L}$$

Where:

$$l$$ = total wire length (m)
$$N$$ = number of turns
$$D$$ = average diameter of the coil (m)
$$A$$ = cross-sectional area of wire (m²)
$$\rho$$ = resistivity of conductor (Ω·m)
$$R$$ = wire resistance (Ω)
$$m$$ = wire mass (kg)
$$\gamma$$ = density of conductor material (kg/m)
$$n$$ = turns per meter
$$L$$ = length of the coil (m)

Physical Properties of Coil – Calculation Example

Given:

$$N$$ = 200 turns
$$D$$ = 0.04 m
$$wire diameter d$$ = 0.5 mm = 0.0005 m
$$\rho (copper)$$ = $$1.68 × 10^{-8} Ω·m$$
$$\gamma (copper)$$ = $$8.96 × 10^3 kg/m³$$
$$L$$ = 0.1 m

Calculation:

$$l = 200 \cdot \pi \cdot 0.04 ≈ 25.13~m $$
$$A = \pi \cdot \left( \frac{0.0005}{2} \right)^2 ≈ 1.96 \cdot 10^{-7}~\text{m}^2 $$
$$R = 1.68 \cdot 10^{-8} \cdot \frac{25.13}{1.96 \cdot 10^{-7}} ≈ 2.15~Ω $$
$$\gamma_{\text{linear}} = \gamma \cdot A = 8.96 \cdot 10^3 \cdot 1.96 \cdot 10^{-7} ≈ 1.75~\text{kg/m}$$
$$m = 25.13 \cdot 1.75 ≈ 43.97~\text{g} $$
$$n = \frac{200}{0.1} = 2000~\text{turns/m}$$

Understanding the physical properties of a coil is essential when designing inductors, transformers, electromagnets, or RF coils. This calculator helps estimate wire length, resistance, and weight before winding, allowing for precise material planning and thermal/electrical efficiency assessment. It supports different conductor materials by adjusting resistivity and density values, making it ideal for practical engineering and educational use.

Physical Properties of Coil Calculator

Coil Geometry and Material Properties Estimator

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Physical Coil Formulas

Physical Properties of Coil – Calculation Example

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