You can calculate the amount of wire of width W needed to make a coil of radius R and length L by using the formula 2?R x (L/W). This formula is equivalent to the circumference each loop of the wire makes times the number of such loops in the coil. This formula is, however, a first approximation. It doesn’t take into consideration the pitch, or slant, of the wire. You can easily derive a more accurate formula by using the Pythagorean theorem.

Draw a diagram of a shallow (short) right triangle, with the base and right angle on the bottom and hypotenuse above.

Denote its base as the length of wire in one turn of the coil if there was no pitch; in other words, the 2?R circumference mentioned in the Overview.

## Sciencing Video Vault

Denote the other side making up the right angle as W, since this is how much higher the wire is after going around one turn of the coil. The hypotenuse therefore represents the unfolding of one turn of the wire in the coil. Denote it as H.

Calculate the hypotenuse’s length, H, by using the Pythagorean theorem. Therefore, H^2 = W^2 + (2?R)^2.

Replace H for 2?R in the formula in the introduction to get ?[ W^2 + (2?R)^2 ] x (L/W). This is the length of the wire needed to form a coil of length L and radius R with wire of width W.

#### Tip

To determine the number of turns, n, needed in the coil to produce a certain magnetic field strength, B, along its axis, use the formula B=?ni, where ? is the magnetic permeability constant and i is the current running through the wire.