Math questions don’t usually require advanced formulas—what they punish is careless setup, unit mistakes, and confusing markup vs margin. This cheat sheet covers the highest-yield calculations contractors see across many licensing exams.
Always confirm your exam’s calculator rules and topic outline in your bulletin.
Quick links
1) Area & volume (the backbone of estimating)
- Area (rectangle): L × W
- Area (triangle): (b × h) ÷ 2
- Volume (rectangular): L × W × H
- Cubic yards: cubic feet ÷ 27
2) Concrete quick math
- Slab volume (ft³): L × W × thickness (ft)
- Convert thickness: inches ÷ 12 = feet
- Order buffer: add 5–10% for waste/spillage (project dependent)
3) Roof quantities
- Roofing square: 100 ft²
- Waste factor: increases with hips/valleys and cut-up roofs
4) Slope / pitch basics
- Slope: rise ÷ run
- Pitch language: “4:12” means 4 inches rise per 12 inches run
5) Unit conversions (quiet score boosters)
- 1 ft = 12 in
- 1 yd = 3 ft
- 1 yd³ = 27 ft³
- 1 gallon = 128 oz (useful for coatings questions)
6) Markup vs margin (don’t mix these up)
This shows up constantly in Business & Law and estimating questions.
- Markup = Profit ÷ Cost
- Margin = Profit ÷ Selling Price
Example: Cost $10,000. Add $2,000 profit. Selling price $12,000.
Markup = 2,000 ÷ 10,000 = 20%
Margin = 2,000 ÷ 12,000 = 16.67%
10 practice problems (with answers)
- Slab: 20 ft × 30 ft × 4 in thick. How many yd³?
Answer: thickness 4/12 = 0.333 ft. Volume = 20×30×0.333 = 199.8 ft³. Yd³ = 199.8/27 = 7.4 yd³ (round up per ordering rules). - Area: A room is 14 ft × 18 ft. What’s the area?
Answer: 252 ft². - Triangle: A gable triangle is 24 ft base and 6 ft height. Area?
Answer: (24×6)/2 = 72 ft². - Roofing squares: A roof is 2,400 ft². How many squares?
Answer: 2,400/100 = 24 squares (add waste as required). - Markup: Cost is $8,000. You want 25% markup. Sell price?
Answer: Profit = 8,000×0.25 = 2,000. Price = 10,000. - Margin: You sell for $15,000 and want 20% margin. What’s max cost?
Answer: Profit = 15,000×0.20 = 3,000. Max cost = 12,000. - Conversion: Convert 96 inches to feet.
Answer: 96/12 = 8 ft. - Volume: A footing trench is 40 ft long, 2 ft wide, 1 ft deep. yd³?
Answer: 40×2×1 = 80 ft³. 80/27 = 3.0 yd³. - Slope: Rise 18 inches over run 12 ft. Slope (as decimal)?
Answer: 18 in = 1.5 ft. 1.5/12 = 0.125. - Waste: You need 500 ft² of tile and add 8% waste. How many ft² to order?
Answer: 500×1.08 = 540 ft².
How to get faster (the exam skill)
- Rewrite the question in your own words
- Write units next to every number (ft, in, yd³)
- Estimate the rough answer first (sanity check)
- Do timed sets and track what slowed you down
Practice under time
Math becomes easy when your setup is automatic. That’s what timed reps build.
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FAQ
Do contractor exams allow calculators?
Rules vary. Some allow basic calculators, others provide on-screen calculators. Always verify in your bulletin.
What’s the #1 math mistake on exams?
Unit errors (inches vs feet) and confusing markup with margin.