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newSchoolWorks.com › VoTechWorks › Building & Construction › Solar / PV Installation › Universal Core: Safety, Math, Communication & Career for Solar PV Installation › Lesson 3
BLD-SOLA09-01 · Lesson 3 · 24 clock hours · theory

Trade Math for Solar PV: Arithmetic, Algebra, and Unit Conversion

Objective. Students will solve trade math problems involving whole numbers, fractions, decimals, percentages, ratios, unit conversion between imperial and metric systems, and algebraic manipulation of Ohm's Law and the power equation (P = IV) as they arise in PV system sizing and wiring calculations.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Why Math Matters in Solar PV Work

Every PV installation involves numbers. You calculate how many modules fit on a roof, whether a wire is sized correctly, and whether a string of modules will exceed an inverter's maximum input voltage. Errors in these calculations can damage equipment, create fire hazards, or result in a system that underperforms. Accurate trade math is therefore a safety skill, not just a bookkeeping task.

Whole Numbers, Fractions, and Decimals

Most PV calculations use decimals because electrical values are rarely round numbers. A module might produce 9.83 A of short-circuit current or have an efficiency of 20.4%. Practice moving between these forms. When adding or subtracting decimals, align the decimal points. When multiplying, count total decimal places in both factors and place the decimal that many positions from the right in your answer.

Fractions appear less often in field calculations, but understanding them helps when reading efficiency ratings expressed as ratios. A system that converts 20 out of every 100 watts of sunlight into electricity has an efficiency of 20/100, or 0.20, or 20%.

Percentages and Efficiency

Percentage means "per hundred." To convert a percentage to a decimal, divide by 100 (move the decimal two places left). To convert a decimal to a percentage, multiply by 100.

In PV work, percentages describe efficiency, derate factors, and temperature-related losses. For example, if a 400 W module operates at 85% of its rated output due to shading and soiling, its actual output is 400 × 0.85 = 340 W. Knowing how to apply a percentage as a multiplier is one of the most frequently used skills on the job.

Ratios and Proportions

A ratio compares two quantities. The DC-to-AC ratio (also called the inverter loading ratio) compares the total DC nameplate capacity of the array to the AC output rating of the inverter. A ratio of 1.2:1 means for every 1 W of inverter capacity you have 1.2 W of modules. Setting up a proportion lets you solve for an unknown when three of the four values are known, using cross-multiplication.

Unit Conversion: Imperial and Metric

The US electrical trade uses both systems. Wire lengths may be measured in feet; module dimensions appear in millimeters; irradiance is expressed in watts per square meter (W/m²). You must convert fluently.

Key relationships to memorize:

To convert, multiply by the correct conversion factor written as a fraction so the unwanted unit cancels. For example, to convert 15 feet to meters: 15 ft × (1 m / 3.281 ft) = 4.57 m.

Ohm's Law

Ohm's Law states the relationship among voltage (V, in volts), current (I, in amperes), and resistance (R, in ohms):

V = I × R

You can rearrange it algebraically to solve for any unknown:

In wiring calculations, you use Ohm's Law to find voltage drop across a conductor. A high voltage drop reduces system efficiency and can be a code compliance issue. Always confirm that conductor sizing keeps voltage drop within acceptable limits for the system design.

The Power Equation: P = IV

Electrical power (P, in watts) equals current times voltage:

P = I × V

Rearrange to find current or voltage when power is known:

This equation is central to PV sizing. If a charge controller must handle an array producing 3,000 W at 48 V, the current it must carry is 3,000 / 48 = 62.5 A. Undersizing a component based on a math error is a genuine safety hazard—overcurrent can cause insulation failure, arcing, and fire.

String Voltage and Temperature Coefficients

Modules connected in series (a string) add their voltages. A string of 10 modules each with an open-circuit voltage (Voc) of 45.0 V produces a string Voc of 450 V. However, module voltage changes with temperature: voltage rises as the module gets colder and drops as it gets hotter. Manufacturers provide a temperature coefficient for Voc (typically expressed in %/°C or V/°C). You apply this coefficient to the lowest expected temperature to find the maximum string voltage and confirm it does not exceed the inverter's maximum DC input voltage—a critical safety check to prevent equipment damage and arc-flash risk.

Safe Calculator Use and Estimation

Always estimate your answer before calculating. If you expect roughly 400 W and your calculator shows 40,000 W, you made a decimal or unit error. Double-check entries and watch for common mistakes: forgetting to convert kW to W, or mixing up Voc and Vmp. Treat a number that seems unreasonably large or small as a red flag and recheck your work.

Summary

Trade math for solar PV is applied arithmetic and basic algebra in an electrical context. Master percentages, unit conversion, Ohm's Law, and P = IV and you will have the quantitative foundation for every sizing, wiring, and safety calculation in this program and on the NABCEP exams.

Key terms8

Ohm's LawThe relationship V = I × R, which states that voltage equals current multiplied by resistance; can be rearranged to solve for any one of the three quantities.
Power equation (P = IV)The formula stating that electrical power in watts equals current in amperes multiplied by voltage in volts; rearranged as I = P/V or V = P/I to solve for unknowns in PV sizing.
Open-circuit voltage (Voc)The maximum voltage a PV module produces when no load is connected; used to calculate maximum string voltage for inverter compatibility and safety checks.
Temperature coefficientA value provided by the module manufacturer (typically in %/°C or V/°C) that describes how voltage or current changes with module temperature; applied to find worst-case string voltage at low temperatures.
Derate factorA multiplier less than 1.0 applied to a system's rated output to account for real-world losses such as soiling, wiring resistance, inverter efficiency, and shading.
DC-to-AC ratioThe ratio of an array's total DC nameplate capacity to the inverter's AC output rating; used in system design to evaluate how closely the array is matched to the inverter.
Unit conversionThe process of expressing a quantity in different units of the same dimension (e.g., watts to kilowatts, feet to meters) by multiplying by a conversion factor that equals 1.
Voltage dropThe reduction in voltage along a conductor caused by the conductor's resistance; calculated using Ohm's Law and used to verify that wiring meets code and performance requirements.

Worked examples4

1. A PV array has a total DC nameplate capacity of 6,500 W. Convert this value to kilowatts, then calculate the array's actual output if it operates at 82% of rated capacity due to system losses.
  1. Step 1 – Convert watts to kilowatts: divide by 1,000. 6,500 W ÷ 1,000 = 6.5 kW.
  2. Step 2 – Convert the percentage to a decimal multiplier: 82% ÷ 100 = 0.82.
  3. Step 3 – Multiply rated capacity by the derate factor: 6.5 kW × 0.82 = 5.33 kW.
  4. Step 4 – Estimate check: 82% of 6.5 is slightly less than 6.5 but more than 5; 5.33 kW is reasonable.
Answer: 5.33 kW actual output.
2. A string of 12 PV modules each has a Voc of 41.5 V at standard test conditions. The temperature coefficient for Voc is −0.30%/°C, and the lowest expected ambient temperature is −10 °C. Standard test condition temperature is 25 °C. Calculate the maximum string Voc at the lowest expected temperature.
  1. Step 1 – Find the temperature difference from STC to the lowest expected temperature: 25 °C − (−10 °C) = 35 °C colder than STC.
  2. Step 2 – Calculate the percentage change in Voc: 35 °C × 0.30%/°C = 10.5% increase (voltage rises as temperature drops).
  3. Step 3 – Convert to a multiplier: 1 + (10.5 ÷ 100) = 1.105.
  4. Step 4 – Find adjusted module Voc: 41.5 V × 1.105 = 45.86 V.
  5. Step 5 – Multiply by the number of modules in series: 45.86 V × 12 = 550.3 V.
  6. Step 6 – Estimate check: 12 × 41.5 = 498 V at STC; a modest increase to about 550 V for a cold day is plausible.
Answer: Maximum string Voc ≈ 550.3 V at −10 °C.
3. A rooftop combiner box will carry the output of an array producing 4,800 W at a system voltage of 240 V DC. Use the power equation to find the current the wiring and overcurrent protection must handle.
  1. Step 1 – Write the rearranged power equation to solve for current: I = P ÷ V.
  2. Step 2 – Substitute the known values: I = 4,800 W ÷ 240 V.
  3. Step 3 – Divide: 4,800 ÷ 240 = 20 A.
  4. Step 4 – Estimate check: at 240 V, every 240 W produces 1 A; 4,800 ÷ 240 = 20, which is consistent.
Answer: 20 A.
4. A conduit run from a rooftop combiner to the inverter is measured as 47 feet. Convert this length to meters for use with a metric voltage-drop formula.
  1. Step 1 – Write the conversion factor as a fraction that cancels feet: (1 m / 3.281 ft).
  2. Step 2 – Multiply: 47 ft × (1 m / 3.281 ft) = 47 ÷ 3.281.
  3. Step 3 – Divide: 47 ÷ 3.281 = 14.33 m.
  4. Step 4 – Estimate check: 1 m ≈ 3.28 ft, so roughly 45 ft ÷ 3 = 15 m; 14.33 m is consistent.
Answer: 14.33 meters (rounded to two decimal places).

The math in this lesson3

Learners compute array output at 82% of rated capacity.
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Brush up in the math halls at newSchoolWorks.com:
In class: Complete a structured set of 30 graduated practice problems drawn from real PV contexts: converting watts to kilowatts, calculating percent efficiency loss, converting feet to meters for string-length estimation, and solving for current given power and voltage—students self-check against an answer key and flag problems they could not solve independently for instructor review. · In pairs, use a scientific calculator to work through a simplified PV module string worksheet: given module Voc, Vmp, Isc, and Imp values from a real specification sheet, calculate total string voltage at various temperatures using a provided temperature coefficient, and determine whether the string voltage stays within a sample inverter's MPPT range—record results in a formatted calculation sheet. · Play a timed unit-conversion relay game in teams of four: each student receives a card with a measurement in one unit (e.g., 2.4 kW) and must convert it correctly (e.g., to watts, BTU/h, or amps at 240 V) before passing to the next player; instructor tracks accuracy and speed to reinforce fluency.
Materials: Scientific calculators (one per student), trade math workbook or instructor-prepared problem sets referencing PV contexts, real PV module specification sheets (at least two different modules), unit conversion reference card, whiteboard and markers for worked examples, answer keys
Check: Graded 25-question math quiz covering all topic areas in the lesson; problems are drawn from PV contexts identical in style to practice sets. Pass mark: 75% (19/25 correct). Students scoring below 75% complete targeted remediation problems and retest within one week.

Practice check8

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

PV System Concepts and System Design
1. A PV module is rated at 380 W. The system's overall derate factor is 0.78. What is the module's expected real-world output?
Electrical Theory
2. Which formula correctly rearranges the power equation P = IV to solve for current?
PV System Concepts and System Design
3. A string of 10 modules each has a Voc of 44.8 V at standard test conditions. What is the string's total Voc?
Electrical Safety and Code Compliance
4. Why is it critical to calculate maximum string voltage at the lowest expected temperature rather than at standard test conditions?
Trade Math and Measurement
5. A conductor run is 62 feet long. Approximately how many meters is that?
PV System Concepts and System Design
6. An inverter has an AC output rating of 5,000 W. The array connected to it has a total DC nameplate capacity of 6,250 W. What is the DC-to-AC ratio?
PV System Concepts and System Design
7. A PV system produces 8,760 kWh of energy in one year. A homeowner's annual electricity use is 10,950 kWh. What percentage of the homeowner's electricity use does the PV system offset?
Electrical Theory
8. Using Ohm's Law, if a DC circuit has a voltage of 48 V and a resistance of 0.6 Ω, what current flows through the circuit?
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