Formulas on the job

Why it matters

Trade work runs on a handful of formulas. Electricians use Ohm's lawThe relationship V = I x R between voltage, current and resistance in a circuit. and the power formulaP = V x I, giving the rate energy is used in watts. to size circuits, choose breakers and troubleshoot. Mechanics use area to work out the force from a hydraulic cylinder or how much material covers a surface. You do not need to love algebra, but you do need to substitute numbers correctly, keep units straight, and rearrange a formula to find the value you are missing.

Core idea 1: Ohm's law

Ohm's law links three quantities in a circuit:

• VoltageThe electrical push in a circuit, measured in volts. (V), measured in volts: the electrical "push".
• CurrentHow much charge flows per second, measured in amperes (amps). (I), measured in amperes (amps, A): how much charge flows per second.
• ResistanceHow much a circuit opposes the flow of current, measured in ohms. (R), measured in ohms: how much the circuit opposes the flow.

The formula is V = I x R. Rearranged:

• I = V / R (current = voltage divided by resistance)
• R = V / I (resistance = voltage divided by current)

A memory aid is the triangle with V on top and I and R on the bottom: cover the one you want, and the other two show you whether to multiply or divide.

Example: a 120 V heater element has a resistance of 10 ohms. I = 120 / 10 = 12 A.

Example: a 12 V battery is connected to a 4 ohm lamp. I = 12 / 4 = 3 A.

Core idea 2: the power formula

Power (P) is the rate at which energy is used, in watts (W): P = V x I. Rearranged: I = P / V.

Example: a 1,440 W space heater on a 120 V circuit draws I = 1440 / 120 = 12 A. On a 15 A circuit that is a big share of the capacity. For loads that run for hours (called continuous loadsLoads that run for hours, which the electrical code generally limits to about 80% of the circuit rating.), the electrical code generally limits them to about 80% of the circuit rating, which for 15 A is 12 A. You will learn the exact code rules, and how your state adopts them, in your apprenticeship classes.

Combining the two formulas gives handy variations such as P = I^2 x R and P = V^2 / R. For the heater: P = 120^2 / 10 = 14,400 / 10 = 1,440 W, the same answer.

These numbers describe what an electrician calculates on paper. Measuring voltage or current on real circuits requires the right meter, training and supervision.

Core idea 3: area formulas

• Rectangle: A = length x width. A room 12 ft x 14 ft has A = 168 sq ft.
• Triangle: A = 1/2 x base x height.
• Circle: A = pi x r^2, or, using the diameter, A = pi x d^2 / 4. A circle 2 in across has A = 3.1416 x 1^2 = 3.14 sq in.

Units matter. 1 sq ft = 12 x 12 = 144 sq in, not 12. A 3 ft x 2 ft panel is 6 sq ft or 864 sq in.

Worked example: hydraulic cylinder force (mechanic)

The force a hydraulic cylinder pushes with is Force = Pressure x Area.

• A cylinder has a 2 in bore (inside diameter). Area = pi x 2^2 / 4 = 3.14 sq in.
• The system pressure is 1,000 psi (pounds per square inch).
• Force = 1,000 x 3.14 = about 3,142 lb.

If the bore were 4 in, the area would be pi x 16 / 4 = 12.57 sq in, and the force about 12,566 lb: doubling the diameter quadruples the force. This is why a small hydraulic cylinder can lift so much, and why stored hydraulic pressure must be released and locked out before maintenance.

Worked example: lighting a room (electrician)

A workshop is 20 ft x 30 ft. The lighting design calls for about 1 watt of LED lighting per square foot.

1. Area = 20 x 30 = 600 sq ft.
2. Lighting load = 600 x 1 = 600 W.
3. Current at 120 V = 600 / 120 = 5 A.

The real design follows the drawings and code, but this quick check tells you the plan is reasonable.

A method for any formula

1. Write the formula before touching numbers.
2. List what you know, with units.
3. Rearrange to isolate the unknown.
4. Substitute and calculate.
5. Sanity-check: is the answer in the right units and a believable size? A household appliance drawing 1,200 A is a mistake.

Common mistakes

• Multiplying when you should divide. Use the triangle or rearrange on paper.
• Mixing units: kilowatts with watts, inches with feet, diameter with radius.
• Using the diameter in pi x r^2. Halve it first, or use pi x d^2 / 4.
• Rounding too early. Keep full precision until the final answer.
• Treating a calculation as permission. Knowing the current a circuit should draw does not make it safe to test it live.

Try it

Open the Do tab. The trade calculator has the power and area formulas written for you. Your job is one line: Ohm's law for current.

Quick recap

• Ohm's law: V = I x R, so I = V / R and R = V / I.
• Power: P = V x I, so I = P / V.
• Area: rectangle L x W; circle pi r^2 or pi d^2 / 4; 1 sq ft = 144 sq in.
• Force from a cylinder = pressure x area.