🔢 Construction Math Reference
Quick conversions, formulas, and calculations for the field.
Area Conversions
| From | To | Multiply By |
|---|---|---|
| Square feet | Square yards | 0.1111 (÷ 9) |
| Square yards | Square feet | 9 |
| Square feet | Square meters | 0.0929 |
| Square meters | Square feet | 10.764 |
| Acres | Square feet | 43,560 |
| Square feet | Acres | 0.0000229 (÷ 43,560) |
Quick Area Formulas
Rectangle: Area = Length × Width
Triangle: Area = (Base × Height) ÷ 2
Circle: Area = π × radius² = 3.14159 × r²
Trapezoid: Area = [(Top + Bottom) ÷ 2] × Height
Volume Conversions
| From | To | Multiply By |
|---|---|---|
| Cubic feet | Cubic yards | 0.037 (÷ 27) |
| Cubic yards | Cubic feet | 27 |
| Cubic feet | Gallons | 7.48 |
| Gallons | Cubic feet | 0.1337 |
| Cubic meters | Cubic yards | 1.308 |
| Cubic yards | Cubic meters | 0.7646 |
Quick Volume Formulas
Rectangular: Volume = L × W × H
Cylinder: Volume = π × r² × H
Cone: Volume = (π × r² × H) ÷ 3
Sphere: Volume = (4/3) × π × r³
Length Conversions
| From | To | Multiply By |
|---|---|---|
| Inches | Feet | 0.0833 (÷ 12) |
| Feet | Inches | 12 |
| Feet | Yards | 0.333 (÷ 3) |
| Yards | Feet | 3 |
| Feet | Meters | 0.3048 |
| Meters | Feet | 3.281 |
| Miles | Feet | 5,280 |
Decimal Feet Conversion
| Fraction | Decimal |
|---|---|
| 1/16" | 0.005' |
| 1/8" | 0.010' |
| 1/4" | 0.021' |
| 3/8" | 0.031' |
| 1/2" | 0.042' |
| 5/8" | 0.052' |
| 3/4" | 0.063' |
| 7/8" | 0.073' |
| 1" | 0.083' |
| 2" | 0.167' |
| 3" | 0.250' |
| 4" | 0.333' |
| 5" | 0.417' |
| 6" | 0.500' |
Weight Conversions
| From | To | Multiply By |
|---|---|---|
| Pounds | Kilograms | 0.4536 |
| Kilograms | Pounds | 2.205 |
| Tons (short) | Pounds | 2,000 |
| Tons (metric) | Pounds | 2,205 |
| Tons (short) | Tons (metric) | 0.907 |
Common Material Weights
| Material | Weight |
|---|---|
| Concrete | 150 lbs/cu ft |
| Steel | 490 lbs/cu ft |
| Water | 62.4 lbs/cu ft (8.34 lbs/gal) |
| Sand (dry) | 100 lbs/cu ft |
| Gravel | 105 lbs/cu ft |
| Soil (average) | 100 lbs/cu ft |
| Lumber (average) | 35 lbs/cu ft |
| Drywall (1/2") | 1.8 lbs/sq ft |
| Plywood (3/4") | 2.3 lbs/sq ft |
Concrete Calculations
Cubic Yards
Cubic Yards = (L' × W' × Thickness") ÷ 324
Or: (L' × W' × D') ÷ 27
Quick Thickness Chart (per 100 SF)
| Thickness | Cubic Yards |
|---|---|
| 2" | 0.62 CY |
| 3" | 0.93 CY |
| 4" | 1.23 CY |
| 5" | 1.54 CY |
| 6" | 1.85 CY |
| 8" | 2.47 CY |
| 10" | 3.09 CY |
| 12" | 3.70 CY |
Bags of Concrete
| Bag Size | Cubic Feet | Bags per CY |
|---|---|---|
| 40 lb | 0.30 | 90 |
| 60 lb | 0.45 | 60 |
| 80 lb | 0.60 | 45 |
Slope & Grade
Slope Conversion
| Ratio | Percent | Degrees | Rise per Foot |
|---|---|---|---|
| 1:12 | 8.3% | 4.8° | 1" |
| 2:12 | 16.7% | 9.5° | 2" |
| 3:12 | 25% | 14° | 3" |
| 4:12 | 33.3% | 18.4° | 4" |
| 5:12 | 41.7% | 22.6° | 5" |
| 6:12 | 50% | 26.6° | 6" |
| 8:12 | 66.7% | 33.7° | 8" |
| 10:12 | 83.3% | 39.8° | 10" |
| 12:12 | 100% | 45° | 12" |
Grade Calculations
Percent Grade = (Rise ÷ Run) × 100
Rise = Run × (Percent ÷ 100)
Run = Rise ÷ (Percent ÷ 100)
Example: 2% grade over 100 feet = 2 foot rise
Roof Calculations
Roof Area Multiplier
| Pitch | Multiplier |
|---|---|
| Flat | 1.00 |
| 2:12 | 1.01 |
| 3:12 | 1.03 |
| 4:12 | 1.05 |
| 5:12 | 1.08 |
| 6:12 | 1.12 |
| 7:12 | 1.16 |
| 8:12 | 1.20 |
| 9:12 | 1.25 |
| 10:12 | 1.30 |
| 11:12 | 1.36 |
| 12:12 | 1.41 |
Roof Area = Footprint Area × Pitch Multiplier
Rafter Length
Rafter = √(Run² + Rise²)
Or use multiplier:
Rafter = Run × Pitch Multiplier
Stair Calculations
Code Requirements (Typical)
| Element | Residential | Commercial |
|---|---|---|
| Max Riser | 7-3/4" | 7" |
| Min Tread | 10" | 11" |
| Min Width | 36" | 44" |
| Min Headroom | 6'-8" | 6'-8" |
Stair Formula
Number of Risers = Total Rise ÷ Riser Height
Number of Treads = Risers - 1
Total Run = Number of Treads × Tread Depth
Comfort Formula: Riser + Tread = 17" to 18"
Circle & Arc Calculations
Circumference = π × Diameter = 2 × π × Radius
Diameter = Circumference ÷ π
Radius = Diameter ÷ 2
π = 3.14159
Arc Length
Arc Length = (Angle ÷ 360) × Circumference
Pythagorean Theorem
a² + b² = c²
c = √(a² + b²)
Common Construction Triangles
| Base | Height | Diagonal |
|---|---|---|
| 3 | 4 | 5 |
| 6 | 8 | 10 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 9 | 12 | 15 |
3-4-5 Rule: To square a corner, measure 3' on one side, 4' on the other. Diagonal should be exactly 5'.
Percentages
Markup: Selling Price = Cost × (1 + Markup%)
Margin: Selling Price = Cost ÷ (1 - Margin%)
Discount: Sale Price = Original × (1 - Discount%)
Markup vs Margin
| Markup | Margin |
|---|---|
| 10% | 9.1% |
| 15% | 13% |
| 20% | 16.7% |
| 25% | 20% |
| 30% | 23.1% |
| 35% | 25.9% |
| 40% | 28.6% |
| 50% | 33.3% |
Temperature
°F = (°C × 9/5) + 32
°C = (°F - 32) × 5/9
| °F | °C | Significance |
|---|---|---|
| 32 | 0 | Water freezes |
| 40 | 4 | Cold weather concrete limit |
| 50 | 10 | Many coating minimums |
| 70 | 21 | Standard curing temp |
| 90 | 32 | Hot weather concrete |
| 100 | 38 | Heat stress concern |