🚧 Under construction — VoTechWorks is being built. A free tech program — complimentary, as our commitment to get America working.
voTechWorksGrade 13 · a vocational technology learning center, by urbanicity
newSchoolWorks.com › VoTechWorks › Building & Construction › Electrical › Universal Core: Safety, Trade Math, Communication & Career Readiness for Electricians › Lesson 4
BLD-ELEC05-01 · Lesson 4 · 20 clock hours · theory

Trade Math II: Percentages, Ratios, Basic Algebra, and Electrical Formulas

Objective. Learners will apply Ohm's Law (V = IR), the power formula (P = IV), and percentage-based calculations to solve entry-level electrical problems with at least 80% accuracy.

Why Trade Math Matters in Electrical Work

Electricians work with invisible forces. You cannot see voltage, current, or resistance—you calculate them. Mistakes in math lead to undersized wire, tripped breakers, overheated conductors, and electrocution hazards. Accurate trade math is not a classroom exercise; it is a safety practice. Every formula in this lesson connects directly to decisions you will make on the job.

Ohm's Law: V = IR

Ohm's Law describes the relationship among three fundamental electrical quantities:

The formula is: V = I × R

Rearrange it to solve for any unknown:

A simple memory tool is the Ohm's Law wheel (sometimes called the formula triangle). Cover the quantity you want to find; what remains shows the operation to perform.

Safety connection: If resistance in a circuit drops unexpectedly—due to a damaged conductor or a short circuit—current rises sharply. High current means heat, and heat means fire or shock. Understanding V = IR helps you recognize why code limits on wire sizing and overcurrent protection exist.

The Power Formula: P = IV

Power (P) is the rate at which electrical energy is converted to another form (heat, light, motion). It is measured in watts (W).

The basic power formula is: P = I × V

Combine it with Ohm's Law to get two more useful forms:

These four formulas—Ohm's Law plus the three power expressions—appear on a combined formula wheel used throughout the trade.

Safety connection: Overcurrent protection devices (fuses, circuit breakers) are rated in amperes, but the damage they prevent is caused by excess power (heat). Knowing how power relates to current and resistance explains why a 20-ampere circuit protected by a 20-ampere breaker must not be continuously loaded beyond 80 percent of that rating (a rule you will study in the NEC in Course 3).

Percentages in Electrical Work

Three percentage calculations appear constantly on the job:

1. Voltage drop as a percentage of source voltage

Voltage drop is the loss of voltage along a conductor due to its resistance. Express it as:

> Voltage Drop % = (Voltage Drop ÷ Source Voltage) × 100

The NEC recommends keeping voltage drop to no more than 3 percent on a branch circuit and no more than 5 percent on the combined feeder-and-branch-circuit run. Exceeding these values causes equipment to run hot and inefficiently.

2. Load as a percentage of panel capacity

> Load % = (Connected Load in Amps ÷ Panel Ampere Rating) × 100

A 200-ampere panel loaded with 180 amperes is at 90 percent capacity—too high for continuous operation without careful review.

3. Derating factors

When conductors are bundled together or routed through high-temperature environments, their current-carrying capacity (ampacity) must be reduced by a derating factor expressed as a percentage. For example, if ampacity tables show 90 A for a conductor but a derating factor of 80 percent applies, the derated ampacity is 90 × 0.80 = 72 A.

Ratios and Proportions

A ratio compares two quantities. In electrical work, transformer turns ratios describe the relationship between primary and secondary voltages:

> V_primary ÷ V_secondary = Turns_primary ÷ Turns_secondary

If a transformer has a 10:1 turns ratio and the primary is 120 V, the secondary is 12 V. Proportional reasoning also helps you scale wire sizes, conduit fill calculations, and material estimates.

Basic Algebra on the Job

Solving for an unknown in an electrical formula is applied algebra. The process is always the same:

1. Write the formula.

2. Identify the unknown.

3. Rearrange the formula to isolate the unknown.

4. Substitute known values and calculate.

5. Label your answer with the correct unit.

Always double-check your answer by substituting it back into the original formula.

Using Technology as a Check—Not a Crutch

Tools like the Desmos graphing calculator let you visualize relationships. When you graph current (I) on the x-axis versus voltage (V) on the y-axis for a fixed resistance, you get a straight line. The slope of that line equals resistance in ohms. Technology confirms your math but does not replace understanding the formula—inspectors and employers expect you to explain your calculations.

Safe Work Habits During Math-Heavy Tasks

Calculations are often done in the field or in a panel room. Follow these habits:

Key terms8

Ohm's LawThe relationship V = IR, stating that voltage equals current multiplied by resistance; the foundation formula of DC circuit analysis.
Voltage (V)Electrical pressure or potential difference that drives current through a circuit, measured in volts.
Current (I)The flow of electric charge through a conductor, measured in amperes (amps).
Resistance (R)The opposition a material offers to the flow of electric current, measured in ohms (Ω).
Power (P)The rate of electrical energy use or conversion, measured in watts (W); calculated as P = IV.
Voltage DropThe reduction in voltage along a conductor caused by the conductor's resistance; expressed as a percentage of source voltage to evaluate compliance with NEC recommendations.
Derating FactorA percentage multiplier applied to a conductor's rated ampacity to account for conditions such as elevated ambient temperature or bundled conductors.
AmpacityThe maximum continuous current a conductor can carry without exceeding its temperature rating, as listed in NEC ampacity tables.

Worked examples4

1. A circuit has a resistance of 12 Ω and a current of 5 A flowing through it. What is the voltage across the resistance?
  1. Write the formula: V = I × R
  2. Substitute known values: V = 5 A × 12 Ω
  3. Calculate: V = 60
  4. Label the answer with the correct unit: 60 V
Answer: 60 V
2. A 120 V circuit supplies a load. The measured voltage at the load is 115.2 V. What is the voltage drop expressed as a percentage of source voltage?
  1. Find the voltage drop: 120 V − 115.2 V = 4.8 V
  2. Apply the percentage formula: Voltage Drop % = (Voltage Drop ÷ Source Voltage) × 100
  3. Substitute: (4.8 ÷ 120) × 100
  4. Calculate: 0.04 × 100 = 4%
  5. Label the answer: 4% voltage drop
Answer: 4% — this exceeds the NEC recommendation of 3% for a branch circuit and warrants review of conductor sizing.
3. A 120 V circuit draws 8 A. What is the power consumed by the load?
  1. Write the formula: P = I × V
  2. Substitute known values: P = 8 A × 120 V
  3. Calculate: P = 960
  4. Label the answer: 960 W
Answer: 960 W
4. An ampacity table shows a conductor rated at 85 A. A derating factor of 70% applies due to bundling. What is the derated ampacity?
  1. Convert the percentage to a decimal: 70% = 0.70
  2. Multiply rated ampacity by the derating factor: 85 A × 0.70
  3. Calculate: 59.5 A
  4. Label the answer: 59.5 A derated ampacity
Answer: 59.5 A

The math in this lesson2

Learners apply E = IR and P = EI, compute percent voltage drop, and derate 85 A ampacity by 70%.
7.RP.3A-CED.4
Brush up in the math halls at newSchoolWorks.com:
In class: Work through an Ohm's Law formula wheel activity: given any two of voltage, current, and resistance, solve for the third in 15 progressively harder problems, then check answers with a partner using a published answer key. · Solve a set of real-world percentage problems common to the trade—voltage drop expressed as a percentage of source voltage, load as a percentage of panel capacity, derating factors—and discuss how each links to National Electrical Code (NEC) requirements that will be studied in Course 3. · Use a free graphing calculator app (Desmos or equivalent) to graph a linear relationship between voltage and current for a fixed resistance, labeling axes with proper units and writing one sentence interpreting the slope in plain language.
Materials: Scientific calculator, Ohm's Law wheel reference card, instructor-prepared problem sets, smartphones or tablets with Desmos app installed, NCCER Core Curriculum textbook math and electrical theory chapters
Check: Timed 20-question written quiz covering percentages, ratios, Ohm's Law, and power formula; learners must score 80% or higher; one tutored retake available within the week.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NCCER Electrical L1 — Electrical Theory
1. A resistor in a DC circuit has a resistance of 24 Ω and 3 A of current flowing through it. What is the voltage across the resistor?
NCCER Electrical L1 — Electrical Theory
2. A 240 V circuit supplies a heater. The heater's resistance is 40 Ω. How much current does the heater draw?
NCCER Electrical L1 — Electrical Theory
3. A load draws 15 A from a 120 V source. What is the power consumed?
NCCER Electrical L2 — NEC and Load Calculations
4. The voltage measured at the end of a branch circuit is 113.6 V on a 120 V source. What is the voltage drop percentage?
NCCER Electrical L2 — NEC and Load Calculations
5. A panelboard is rated at 200 A. The total connected load is 160 A. What percentage of panel capacity is in use?
NCCER Electrical L2 — NEC and Load Calculations
6. A conductor has a rated ampacity of 100 A. A derating factor of 80% is required. What is the maximum allowable continuous current for this conductor after derating?
NCCER Electrical L1 — Electrical Theory
7. When graphing voltage (V) on the y-axis versus current (I) on the x-axis for a fixed resistance, what does the slope of the resulting straight line represent?
OSHA 10 — Electrical Hazards and Safe Work Practices
8. Before measuring the resistance of a conductor that is part of an installed circuit, what is the most important safety step an electrician must take?
Record this lesson on my transcript. Sign in with your key and enrollment email to record lessons (enroll free if you have no key). This page stays open to read and practise.
← Previous lessonProgram planNext lesson →