Trade Math and Imperial Fractions Reference

Why this matters

US trades work in imperial units with fractions - feet, inches, sixteenths, eighths. Most measurements aren't whole inches. Knowing how to add 5'3-5/8" to 2'7-3/4" without a calculator, how to convert between fractions and decimals, and basic geometry (Pythagorean theorem for roofing, area for material estimates) is foundational. The math is simple but slow if you don't practice it; fast and accurate if you do.

The standard imperial fractions

For converting between fractions and decimals: numerator ÷ denominator. 3/8 = 0.375. 5/16 = 0.3125.

Adding fractions

Same denominator (common case): 3/8 + 1/8 = 4/8 = 1/2

Different denominators (find common denominator): 3/8 + 1/4 Convert 1/4 to 2/8: 3/8 + 2/8 = 5/8

3/4 + 5/16 Convert 3/4 to 12/16: 12/16 + 5/16 = 17/16 = 1-1/16

Common denominator tip: when adding fractions of 1/4 and 1/8 and 1/16, convert everything to 16ths. They all divide evenly.

Adding feet and inches with fractions

Example: 5'3-5/8" + 2'7-3/4"

Step 1: Add inches and fractions separately

• 3-5/8" + 7-3/4" = ?
• Convert 5/8 to 10/16: 3-10/16
• Convert 3/4 to 12/16: 7-12/16
• Add: 10-22/16 = 11-6/16 = 11-3/8" (since 22/16 = 1-6/16)

Step 2: Add feet

• 5' + 2' = 7'

Step 3: Combine, simplify if inches ≥ 12

• 7' 11-3/8" (under 12 inches, no carry)

If inches were say 14-1/4", convert to 1' 2-1/4" and carry to feet.

Subtracting feet and inches

Example: 8'4-3/8" − 3'9-1/2"

Step 1: Subtract inches and fractions

• 4-3/8" − 9-1/2" - can't subtract (4 < 9)
• Borrow 12" from the 8 feet: 7' (4+12)" = 7' 16"
• Now: 16-3/8" − 9-1/2"
• Convert to 16ths: 16-6/16 − 9-8/16 = 6-14/16 = 6-7/8"
  • Hmm, wait: 16-6/16 minus 9-8/16. 6/16 < 8/16. Borrow 1 inch (16/16) from 16: 15-22/16 − 9-8/16 = 6-14/16 = 6-7/8"
• 7' 6-7/8" − 3' = 4' 6-7/8"

Step 2: Subtract feet

• Already done above

Result: 4' 6-7/8"

Measurement and reading the tape

Standard US tape measures show:

• Whole inches with large numbers
• 1/2" marks long
• 1/4" marks medium
• 1/8" marks shorter
• 1/16" marks shortest (sometimes 1/32" on premium tapes)

When measuring, read to the smallest meaningful fraction for your task:

• Trim carpentry, finish work: 1/32" or 1/16"
• Rough framing: 1/4" or 1/8"
• Plumbing rough-in: 1/4" typical
• HVAC ducting: 1/2" typical
• Concrete forms: 1/4" typical

Common imperial conversions

Metric conversions (when working with imported parts or international specs)

Some HVAC equipment uses metric refrigerant line sizes. 1/4" ≈ 6 mm (close but not exact).

Useful geometric formulas

Area of a rectangle: A = L × W (in same units; convert if needed)

Area of a triangle: A = (1/2) × base × height

Area of a circle: A = π × r²

Volume of a rectangular box: V = L × W × H

Volume of a cylinder: V = π × r² × H

Pythagorean theorem (right triangle): a² + b² = c² (where c is the hypotenuse)

For example, a 12-12 roof pitch (12" rise per 12" run):

• Rise² + Run² = Rafter² (hypotenuse)
• 12² + 12² = 144 + 144 = 288
• √288 ≈ 17"
• So a 12-12 pitch rafter is 17" long per 12" run

For a 6-12 pitch (typical residential):

• 6² + 12² = 36 + 144 = 180
• √180 ≈ 13.4"
• So a 6-12 pitch rafter is 13.4" per 12" run

Roof pitch and angle

Square footage estimates (rough check on quotes)

Customer's home is "1800 square feet"? Verify with a few quick measurements:

• Outside walls: about 30 × 60 = 1800 sq ft (single story)
• Or 30 × 30 = 900 sq ft × 2 stories = 1800

If the home is L-shaped or irregular, break into rectangles, calculate each, sum.

Material estimating fractions

Drywall: 4'×8' sheet = 32 sq ft. Wall area / 32 = approximate sheets, then add 10-15% waste.

Shingles: 1 square = 100 sq ft of roof. Most shingle bundles cover 1/3 square, so 3 bundles per square.

Sheathing (4'×8' panels): 32 sq ft per panel. Same calculation as drywall.

Concrete: in cubic feet for small jobs; cubic yards for slabs / footings. 1 yard = 27 cu ft.

Tile: measure floor area in square inches (or feet), divide by tile area, add 10% waste.

Pipe / conduit: measure run length, add 10% for fittings, cutting waste.

Math shortcuts every tech should know

Doubling and halving fractions:

• 1/4 doubled = 1/2
• 1/2 halved = 1/4
• 3/4 halved = 3/8 (numerator stays the same, denominator doubles)
• 7/8 doubled = 7/4 = 1-3/4

Quick decimal-fraction conversions:

• 0.0625 = 1/16 (about 1/16)
• 0.125 = 1/8
• 0.25 = 1/4
• 0.333... = 1/3
• 0.375 = 3/8
• 0.5 = 1/2
• 0.625 = 5/8
• 0.667... = 2/3
• 0.75 = 3/4
• 0.875 = 7/8

Quick mental math for trade applications:

• 80% of a number: easier to multiply by 0.8 OR subtract 20%
• Continuous load (125%): add 1/4 of the load
• Markup 33% (margin 25%): multiply by 1.33
• Markup 50% (margin 33%): multiply by 1.5
• Markup 100% (margin 50%): double

Common measurement mistakes

• Reading the wrong side of the tape. "Inside" vs "outside" of the hook matters.
• Treating diagonal as length. When measuring a square table from corner to corner, you get the diagonal (longer), not the side.
• Mixing units mid-measurement. Start in inches; finish in inches. Don't mix with metric without conversion.
• Reading 5/8" as 5/16". Easy mistake; double-check at small fractions.
• Not accounting for the kerf when cutting. A saw blade removes ~1/8" of material; multiple cuts add up.
• Forgetting to add or subtract material thickness. Sheetrock screws into studs but the rock itself adds 1/2" to wall depth.

Tools

References

• US Customary Units (NIST)
• Engineering Tool Box (online calculator references)
• "Mathematics for the Trades" textbooks (industry standard)
• ASTM mathematics references for construction