Electrician Math: The Formulas You Actually Use on the Job

Most electrician math formulas come down to a few calculations you will use for your whole career. You do not need calculus. You need to be quick and confident with Ohm's law, voltage drop, box fill and conduit bending, because those questions come up on the job every week and on every licensing exam. This guide works through each one with real numbers so you can check your own work.

One rule first: code tables change between editions. The box fill values below come from Table 314.16(B) as published in the 2020 NEC. Always check against the edition your jurisdiction has adopted.

Ohm's law and the power formulas

Ohm's law relates voltage (V, sometimes written E), current (I) and resistance (R):

• V = I x R
• I = V / R
• R = V / I

The power formulas are the other half:

• P = V x I (watts = volts x amps)
• P = I² x R
• P = V² / R

Worked example: what does a 1,500-watt heater draw?

A customer wants to plug in a 1,500 W space heater at 120 V. Use I = P / V: 1,500 / 120 = 12.5 amps. On a 15 A circuit that already serves a few other loads, you can see right away why that breaker keeps tripping.

The heating element's resistance is R = V / I: 120 / 12.5 = 9.6 ohms. If you meter the element cold and read something far from that, the element is probably the problem.

The voltage drop formula, worked step by step

Voltage drop is just Ohm's law applied to the wire itself. The wire has resistance, current flows through it, and some voltage is lost before it reaches the load. The common working formulas, as shown by calculator.net's voltage drop calculator, are:

• Single-phase: VD = 2 x I x R x L
• Three-phase: VD = 1.732 x I x R x L

I is the load current, R is the conductor's resistance per 1,000 feet, and L is the one-way length in thousands of feet. The 2 is there because current travels out and back. In a balanced three-phase circuit, the square root of 3 (1.732) replaces it.

For resistance, a standard AWG table lists copper at 20°C as about 2.525 ohms per 1,000 ft for 14 AWG, 1.588 for 12 AWG, 0.9989 for 10 AWG, 0.6282 for 8 AWG and 0.3951 for 6 AWG. The NEC's Chapter 9 tables give resistance at operating temperature, which is a little higher, so use those numbers for anything that has to pass a plan review.

Example 1: a long 120 V run

Suppose a 16 A load sits 100 feet from the panel on 12 AWG copper at 120 V.

1. VD = 2 x 16 x 1.588 x 0.100 = 5.08 volts
2. Percent drop = 5.08 / 120 = 4.2%
3. Try 10 AWG instead: 2 x 16 x 0.9989 x 0.100 = 3.20 V, or 2.7%

Example 2: a three-phase feeder

Suppose a 40 A load sits 150 feet from the panel at 208 V three-phase.

1. On 8 AWG: 1.732 x 40 x 0.6282 x 0.150 = 6.53 V, or 3.1%
2. On 6 AWG: 1.732 x 40 x 0.3951 x 0.150 = 4.11 V, or 2.0%

What percentage counts as acceptable depends on the job. The project spec or the engineer's design criteria usually set the target, and the informational notes in your code edition give guidance. Calculator.net, for example, recommends staying under 5% at full load. Whatever the target is, the method is the same: calculate, compare and go up one wire size if the result is over.

Box fill calculation (NEC 314.16)

Box fill keeps conductors from being crammed into a box where they overheat or get nicked when the device is pushed back. The method has two steps: count allowances, then multiply by volume.

Step 1: volume per conductor

From Table 314.16(B), as reproduced by Omni's box fill reference (2020 NEC):

Step 2: count the allowances

• Each conductor that enters the box counts as one. Pigtails that stay entirely inside the box do not count.
• Internal cable clamps: one allowance for the whole set. External clamps count zero.
• Support fittings (fixture studs, hickeys): one allowance.
• Each device (switch or receptacle on a yoke): two allowances.
• Equipment grounding conductors: one allowance for up to four, plus one-quarter for each additional one.

Example: a single receptacle with two 12/2 cables

Two 12/2 NM cables come into a box with internal clamps and feed one receptacle.

1. Insulated conductors: 4 (two blacks, two whites)
2. Grounds: 2 grounds = 1 allowance
3. Clamps: 1
4. Receptacle: 2
5. Total: 8 allowances x 2.25 in³ = 18.0 in³ minimum

Check the cubic-inch rating stamped inside the box. If it is under 18.0, use a deeper box or a larger one.

A harder example from the Omni reference has six 12 AWG and two 16 AWG conductors, five 12 AWG grounds, two devices and internal clamps. It comes to 14.25 allowances, or about 32.06 in³ at 12 AWG volume. That points to a 4-11/16 x 2-1/8 square box. If your wire sizes are mixed, the reference says to calculate each part at its own size instead of using the shortcut.

Conduit bending math: offsets and shrink

Offset bends are the most common bending calculation, and they are basic trigonometry. To clear an obstruction, you make two equal bends. The distance between your marks is the offset depth times a multiplier, and the multiplier is the cosecant (1 / sine) of the bend angle.

Bending an offset also makes the pipe come up shorter, which is called shrink. Shrink per inch of offset is the cosecant minus the cotangent, which simplifies to the tangent of half the angle.

Example: a 6-inch offset at 30 degrees

1. Distance between marks: 6 x 2 = 12 inches
2. Shrink: 6 x 0.268 = about 1.6 inches (the 1/4-inch rule of thumb gives 1.5 inches)
3. If the obstruction starts 40 inches from the end of the pipe, add the shrink to place the first mark, at about 41-5/8 inches.

Pick the angle based on the situation. Shallow angles (10° and 22.5°) are easier to pull through and work well for small offsets, but they need a lot of length. Steeper angles fit tight spaces but make the pull harder. Count your degrees as you go: the NEC limits the total bends between pull points to 360 degrees. That is four 90s, or many more offsets than people expect. The conduit overview describes this limit and the use of conduit bodies when you reach it.

Take-up (deduct) for a 90-degree bend depends on your bender and pipe size. Use the value marked on your bender's shoe instead of a number from someone else's chart.

Electrician math cheat sheet

How to get fast at this

Speed comes from repetition on real situations, not memorized worksheets. Try this:

• On every job, do the box fill for at least one box in your head before you choose a device box.
• Before a long run, calculate voltage drop at two wire sizes and compare.
• Write the offset table on a piece of tape on your bender handle until you no longer need it.
• Practice timed calculations before your exam. Our journeyman exam guide covers how the calculation questions are set up, and first-year apprentice mistakes explains why a wrong offset costs more than wasted pipe.

The bottom line