Electrical engineering / Free calculator

Cable & trace inductance

Estimate inductance from conductor geometry. Choose a return-path model, enter dimensions, and review the assumptions behind the result.

01 Your inputs

External loop model: both conductors are included. Enter one-way cable length.

Conductor geometry
Units for every dimension

Changing units converts all entered dimensions, including copper thickness.

Use the selected dimension unit. For cables, enter the routed length once, not the sum of both conductors.

Copper diameter, excluding insulation. For coax, use the centre conductor diameter.

Two-wire: centre-to-centre spacing s. Coax: inside diameter D of the shield, excluding jacket. Must exceed d.

Straight rectangular copper conductor without a defined ground return.

Use the selected unit: 35 µm = 0.035 mm ≈ 0.001378 in. This is copper thickness, not board thickness.

Calculated on your device. Inputs are not transmitted or stored.

02 Your result

Enter your values and select Calculate.

The method

Choose the matching geometry

Dimensions in the equations are in metres; L is in henries. Cable equations describe the external loop. Wire and trace equations describe one conductor’s partial inductance. ln is the natural logarithm; acosh is inverse hyperbolic cosine.

Two-wire cable

Two conductors, one loop

Cross-section · looking along the cable

Two round conductors with diameter d and centre spacing sA dot marks outgoing current in the left wire; a cross marks return current in the right wire. The spacing dimension ends at the two centres, not their edges.

Length view

Length and current directionTwo straight wires run side by side over one cable length l. Arrows point in opposite directions.
Current out of the section Current into the section
Copper
l
One-way cable length
d
Bare conductor diameter, excluding insulation
s
Centre-to-centre wire spacing
The two wires carry equal, opposite currents. Enter the cable length once; the external loop estimate already includes both conductors. Insulation is omitted. Symbolic model; views are not to scale.
L=4×10−7·l·acosh(sd)
Coaxial cable

A concentric return path

Cross-section · looking along the cable

Coax centre conductor and shield inside diameterCopper surrounds a nonmagnetic dielectric. The dot in the centre conductor points out of the section; the cross in the shield points into it. D spans the shield's inner surface.

Longitudinal section

Length and current directionThe centre conductor runs between the upper and lower sections of one surrounding shield. The arrow in the centre points forward; the shield arrows point back. Length l is measured once.
Current out of the section Current into the section
CopperNonmagnetic dielectric
l
One-way cable length
d
Centre conductor diameter
D
Inside diameter of the shield
The centre conductor carries the outgoing current; the shield carries the equal return current. D reaches the inside of the shield, not the jacket. The estimate includes external loop inductance only. Symbolic model; views are not to scale.
L=2×10−7·l·ln(Dd)
Straight round wire

One conductor, partial inductance

Cross-section · looking along the cable

Bare round wire diameterA solid copper circle has diameter d. The dot marks current out of the section. No return conductor is included.

Length view

Length and current directionOne bare straight wire has length l and a forward current arrow. The return path is excluded.
Current out of the section
Copper
l
Straight conductor length
d
Bare conductor diameter, excluding insulation
The return conductor is unspecified and is not drawn. This is partial inductance of one straight wire; a complete circuit depends on the return path and mutual coupling. Symbolic model; views are not to scale.
L=2×10−7·l·(ln(4·ld)−0.75)
Straight PCB trace

Copper trace geometry

Plan view

Copper trace length, width, and current directionA straight copper strip sits on nonconducting board material. The length dimension follows the strip; w spans its width. Current I flows along the copper, not through the board.

Trace cross-section

Rectangular conducting area of the copper traceOnly the copper strip conducts. Its cross-section has width w and copper thickness t. The hatched material beneath is the board, not a return plane.

The copper rectangle is the conducting area A.

CopperBoard material
l
Trace length
w
Trace width
t
Copper thickness, not board thickness
The return conductor and ground-plane coupling are excluded. This is partial inductance, not a complete circuit-loop estimate. Symbolic model; not to scale.
L=2×10−7·l·(ln(2·l(w+t))+0.5+0.2235·(w+t)l)
L=l×Lper metre

A worked example

Two-wire cable: for 1000 mm one-way length, 1 mm bare wire diameter and 3 mm centre spacing, acosh(3) ≈ 1.762747. External loop inductance is 0.7051 µH, or 705.1 nH/m. Do not multiply by two. As an independent trace example, a 1 inch × 0.010 inch × 0.00135 inch conductor gives approximately 28.83 nH (Linear Technology, Figure 6).

Assumptions & limits

Straight, uniform, nonmagnetic conductors in a nonmagnetic medium (µ ≈ µ₀). Wire and trace use uniform-current, low-frequency partial self-inductance estimates; the return path and its mutual coupling are excluded. The trace model is not microstrip or stripline. Cable models give external loop inductance with negligible internal flux; low-frequency internal inductance is excluded. No frequency transition is modelled. Length must be at least 10 times diameter, cable spacing, shield diameter, or trace width + thickness. This gate does not guarantee accuracy. Dimensions must be 10⁻⁹ to 10⁹ in the selected unit; these are numerical limits. Excludes connectors, bends, twisting, magnetic cores, adjacent metal and radiation. Permittivity is not needed for these magnetic estimates. Use a field solver or measurement for a final design, and a transmission-line model when propagation matters.

Calculation source: Engineering Workbench engine 0.3.0; Rosa (1908) slender-wire approximation, Linear Technology May 1996 Figure 6 trace approximation, and ideal TEM cable line constants. Primary references below.

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