The Candidate Information Booklet says knowledge of basic mathematics is required for every part of the construction exams, and the B&F outline lists "labor productivity," "general conditions costs of projects" and "company overhead" under Preparing Bids/Proposals. This page covers the arithmetic behind a bid: contract pricing types, quantity takeoffs, labor and general conditions, and comparing bids. Pricing the overhead and profit on top is covered in job costing and estimating.
Lump sum vs. unit price
| Lump sum (stipulated sum) | Unit price | |
|---|---|---|
| Price | One fixed price for the defined scope | Price per unit (per cubic yard, linear foot, each) |
| Final contract amount | Fixed, adjusted only by change orders | Unit price × actual measured quantity |
| Quantity risk | Contractor | Owner |
| Typical use | Buildings with complete drawings | Sitework, utilities, paving, where quantities are uncertain |
Example: unit price contract
A bid schedule lists 1,850 linear feet (LF) of curb at $22.00 per LF. The bid amount is 1,850 × $22.00 = $40,700. If 2,010 LF is actually installed and measured, payment is 2,010 × $22.00 = $44,220. The unit price stays the same; the quantity changes.
Units and conversions
| Unit | Meaning | Conversion |
|---|---|---|
| SF | Square foot | 1 SY (square yard) = 9 SF |
| CF | Cubic foot | 1 CY (cubic yard) = 27 CF |
| LF | Linear foot | |
| BF | Board foot | 1 in × 12 in × 12 in of lumber (144 cubic inches) |
| SQ | Roofing square | 100 SF |
The single biggest source of wrong answers is forgetting to convert inches to feet before multiplying. Four inches is 4/12 = 0.333 ft; six inches is 0.5 ft.
Concrete takeoff
Volume (CY) = length (ft) × width (ft) × thickness (ft) ÷ 27
Example: slab
A slab is 50 ft × 30 ft × 6 in thick. Allow 10% waste, round up to the next whole yard.
Step 1. Convert thickness. 6 in = 0.5 ft Step 2. Cubic feet. 50 × 30 × 0.5 = 750 CF Step 3. Cubic yards. 750 ÷ 27 = 27.78 CY Step 4. Waste. 27.78 × 1.10 = 30.56 CY Step 5. Order. 31 CY
Example: continuous footing
200 LF of footing, 2 ft wide × 1 ft deep: 200 × 2 × 1 = 400 CF ÷ 27 = 14.81 CY before waste.
Drywall takeoff
Example: one room
A room is 14 ft × 12 ft with 9 ft ceilings. Hang walls and ceiling. Sheets are 4 ft × 8 ft (32 SF). Ignore openings, add 10% waste, round up.
Step 1. Perimeter. 2 × (14 + 12) = 52 LF Step 2. Wall area. 52 × 9 = 468 SF Step 3. Ceiling. 14 × 12 = 168 SF Step 4. Total. 468 + 168 = 636 SF Step 5. With waste. 636 × 1.10 = 699.6 SF Step 6. Sheets. 699.6 ÷ 32 = 21.86, so 22 sheets
If the question says to deduct openings, subtract their area before dividing.
Masonry takeoff
A standard 8 in × 16 in concrete block has a nominal face of 8 × 16 = 128 square inches, or 0.889 SF, so it takes 1.125 blocks per SF of wall.
A wall 100 ft long × 8 ft high = 800 SF × 1.125 = 900 blocks before waste.
Lumber
Board feet = thickness (in) × width (in) × length (ft) ÷ 12
Forty 2×10s, 16 ft long: 2 × 10 × 16 ÷ 12 = 26.67 BF each; × 40 = 1,066.67 BF. At $0.95 per BF, the material cost is 1,066.67 × $0.95 = $1,013.33 before tax. (Nominal dimensions are used for board feet.)
Labor from productivity
Labor hours = quantity ÷ production rate × crew size × hours per day (when the rate is per crew-day)
Example
A 2-person crew installs 400 SF of tile per 8-hour day. The job is 3,200 SF. Burdened labor is $38 per worker-hour.
Step 1. Crew-days. 3,200 ÷ 400 = 8 days Step 2. Worker-hours. 8 days × 2 workers × 8 hours = 128 hours Step 3. Labor cost. 128 × $38 = $4,864
Counting only one worker ($2,432) is the common error.
General conditions
Time-related job costs are priced by duration.
A superintendent at $2,000 per week, a job trailer at $250 per week and temporary toilets at $90 per week, on a 30-week schedule:
($2,000 + $250 + $90) × 30 = $2,340 × 30 = $70,200
If the schedule slips, these costs keep running. That is why delay costs are real money (see construction contracts).
Putting a small bid together
| Item | Amount |
|---|---|
| Materials (from takeoff, with waste) | $62,000 |
| Sales tax on materials at an assumed 7% | $4,340 |
| Labor (burdened) | $48,000 |
| Subcontracts | $35,000 |
| Equipment | $6,500 |
| General conditions | $14,200 |
| Direct cost | $170,040 |
Overhead and profit are then added as shown in job costing and estimating. The 7% sales tax rate here is only for illustration; use whatever rate a question gives you.
Comparing bids: base bid and alternates
When an owner asks for a base bid plus alternates and accepts some of them, the low bidder is determined on the base bid plus the accepted alternates.
| Base bid | Alternate 1 (accepted) | Total | |
|---|---|---|---|
| Bidder A | $640,000 | +$30,000 | $670,000 |
| Bidder B | $652,000 | +$14,000 | $666,000 |
Bidder A is low on the base bid, but Bidder B is low once the accepted alternate is included. AIA A701, Instructions to Bidders, is on the B&F reference list; questions about how bids are compared, how words and figures conflicts are resolved, or what happens to bid security are answered from your copy of that document.
Checklist for any takeoff question
- Convert every dimension to the same unit (usually feet).
- Compute area or volume.
- Convert to the ordering unit (CY, sheets, squares, blocks).
- Apply waste only if the question says to.
- Round up only at the end, and only if the question says to.
Practice takeoff math
Our Florida Business and Finance Exam Prep includes original takeoff, productivity and bid comparison questions with every step shown, plus 90 days of practice across the full exam. Related: time value of money and the B&F exam overview.
Practice questions
A slab is 60 ft x 40 ft x 4 inches thick. Allowing 5% waste, how many cubic yards of concrete should be ordered (round up to the next whole yard)?
- A30 cubic yards
- B32 cubic yards
- C89 cubic yards
- D27 cubic yards
Show answer
Answer: B. Volume = 60 x 40 x (4/12) = 800 cu ft; / 27 = 29.63 cu yd; x 1.05 = 31.11, rounded up to 32. 89 comes from forgetting to convert inches to feet.
Source: Standard accounting/construction-management principle
A wall is 120 ft long and 8 ft high, with 2 openings totaling 60 sq ft. Drywall comes in 4x8 sheets. Ignoring waste, how many sheets are needed for one side (round up)?
- A29 sheets
- B30 sheets
- C32 sheets
- D28 sheets
Show answer
Answer: A. Net area = 120 x 8 - 60 = 900 sq ft; / 32 sq ft per sheet = 28.1, rounded up to 29 sheets. 30 ignores the openings (960/32).
Source: Standard accounting/construction-management principle
An estimate calls for 2,450 board feet of lumber priced at $0.85 per board foot. The material cost before tax is:
- A$2,082.50
- B$2,882.35
- C$2,450.00
- D$1,960.00
Show answer
Answer: A. Cost = 2,450 x $0.85 = $2,082.50. $2,882.35 divides by 0.85 instead of multiplying.
Source: Standard accounting/construction-management principle
A three-person crew hangs 1,200 sq ft of drywall per 8-hour day. For a 9,600 sq ft job at a burdened labor rate of $30 per worker-hour, what is the estimated labor cost?
- A$1,920
- B$2,400
- C$7,200
- D$5,760
Show answer
Answer: D. Days = 9,600 / 1,200 = 8. Worker-hours = 8 days x 3 workers x 8 hours = 192. Cost = 192 x $30 = $5,760. $1,920 counts only one worker.
Source: Standard labor productivity arithmetic (verified in Python)
A job's general conditions include a superintendent at $1,800 per week and temporary facilities at $400 per week. If the schedule is 26 weeks, what general conditions cost should be carried in the bid?
- A$46,800
- B$57,200
- C$10,400
- D$52,000
Show answer
Answer: B. ($1,800 + $400) x 26 weeks = $2,200 x 26 = $57,200. $46,800 covers only the superintendent, and $10,400 only the temporary facilities.
Source: Standard estimating arithmetic (verified in Python)
An owner requests a base bid and one additive alternate. Bidder A: base $500,000, alternate +$25,000. Bidder B: base $510,000, alternate +$12,000. The owner accepts the alternate. Under AIA A701-2018, how is the low bidder determined, and who is low?
- AOn the base bid alone; Bidder A is low at $500,000
- BOn the sum of base plus alternates; Bidder A is low at $525,000
- COn the sum of the base bid plus accepted alternates; Bidder B is low at $522,000
- DOn the lowest alternate price; Bidder B is low at $12,000
Show answer
Answer: C. A701 §5.3.2 lets the Owner find the lowest responsive and responsible bidder based on the base bid plus accepted alternates. A = $500,000 + $25,000 = $525,000 and B = $510,000 + $12,000 = $522,000, so B is low.
Source: AIA A701-2018 §5.3.2
These are from our bank of 466 original questions. Get the full Florida Business & Finance prep.