Maths for electricians · Topic 1 of 6

Rearranging formulas (transposition)

About 4 minutes · Diagrams, worked examples and a mini test

Most electrical exam questions give you a formula with the wrong thing on its own. Rearranging, or transposition, gets the value you want on one side.

• V – Voltage
• I – Current
• R – Resistance
• P – Power

The golden rule

A formula is a balance. Whatever you do to one side, do to the other. To move something, do the opposite of what's being done to it:

• Multiplied by something? Divide both sides by it.
• Divided by something? Multiply both sides by it.
• Squared? Take the square root of both sides.

Example: find I from V = I × R

I is multiplied by R, so divide both sides by R:

V ÷ R = I × R ÷ R → I = V ÷ R

With V = 230 V and R = 46 Ω: I = V ÷ R = 230 ÷ 46 = 5 A.

The formula triangle shortcut

The formula wheel shows every rearrangement of V, I, R and P in one picture.

For three-part formulas like V = I × R or P = V × I, cover the one you want. Covering I leaves V over R, so I = V ÷ R. Covering V leaves I next to R, so V = I × R.

Formulas with squares

Power can also be written P = I² × R. To find I, first divide by R, then square-root both sides:

I² = P ÷ R → I = √(P ÷ R)

A 1,000 W heater element of 10 Ω: I = √(1000 ÷ 10) = √100 = 10 A.

Longer formulas

Voltage drop is Vd = (mV × Ib × L) ÷ 1000. To find the longest run L, multiply both sides by 1000, then divide by mV and Ib:

L = (1000 × Vd) ÷ (mV × Ib)

Exam tip: write the formula first, rearrange it with letters, and only then put the numbers in. It's much harder to go wrong.

Try it: Ohm's law calculator