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πŸ”’ Construction Math Reference

Quick conversions, formulas, and calculations for the field.

Area Conversions​

FromToMultiply By
Square feetSquare yards0.1111 (Γ· 9)
Square yardsSquare feet9
Square feetSquare meters0.0929
Square metersSquare feet10.764
AcresSquare feet43,560
Square feetAcres0.0000229 (Γ· 43,560)

Quick Area Formulas​

Rectangle:     Area = Length Γ— Width
Triangle:      Area = (Base Γ— Height) Γ· 2
Circle:        Area = Ο€ Γ— radiusΒ² = 3.14159 Γ— rΒ²
Trapezoid:     Area = [(Top + Bottom) Γ· 2] Γ— Height

Volume Conversions​

FromToMultiply By
Cubic feetCubic yards0.037 (Γ· 27)
Cubic yardsCubic feet27
Cubic feetGallons7.48
GallonsCubic feet0.1337
Cubic metersCubic yards1.308
Cubic yardsCubic meters0.7646

Quick Volume Formulas​

Rectangular:   Volume = L Γ— W Γ— H
Cylinder:      Volume = Ο€ Γ— rΒ² Γ— H
Cone:          Volume = (Ο€ Γ— rΒ² Γ— H) Γ· 3
Sphere:        Volume = (4/3) Γ— Ο€ Γ— rΒ³

Length Conversions​

FromToMultiply By
InchesFeet0.0833 (Γ· 12)
FeetInches12
FeetYards0.333 (Γ· 3)
YardsFeet3
FeetMeters0.3048
MetersFeet3.281
MilesFeet5,280

Decimal Feet Conversion​

FractionDecimal
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​

FromToMultiply By
PoundsKilograms0.4536
KilogramsPounds2.205
Tons (short)Pounds2,000
Tons (metric)Pounds2,205
Tons (short)Tons (metric)0.907

Common Material Weights​

MaterialWeight
Concrete150 lbs/cu ft
Steel490 lbs/cu ft
Water62.4 lbs/cu ft (8.34 lbs/gal)
Sand (dry)100 lbs/cu ft
Gravel105 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' Γ— W' Γ— Thickness") Γ· 324

Or: (L' Γ— W' Γ— D') Γ· 27

Quick Thickness Chart (per 100 SF)​

ThicknessCubic 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 SizeCubic FeetBags per CY
40 lb0.3090
60 lb0.4560
80 lb0.6045

Slope & Grade​

Slope Conversion​

RatioPercentDegreesRise per Foot
1:128.3%4.8Β°1"
2:1216.7%9.5Β°2"
3:1225%14Β°3"
4:1233.3%18.4Β°4"
5:1241.7%22.6Β°5"
6:1250%26.6Β°6"
8:1266.7%33.7Β°8"
10:1283.3%39.8Β°10"
12:12100%45Β°12"

Grade Calculations​

Percent Grade = (Rise Γ· Run) Γ— 100
Rise = Run Γ— (Percent Γ· 100)
Run = Rise Γ· (Percent Γ· 100)

Example: 2% grade over 100 feet = 2 foot rise

Roof Calculations​

Roof Area Multiplier​

PitchMultiplier
Flat1.00
2:121.01
3:121.03
4:121.05
5:121.08
6:121.12
7:121.16
8:121.20
9:121.25
10:121.30
11:121.36
12:121.41
Roof Area = Footprint Area Γ— Pitch Multiplier

Rafter Length​

Rafter = √(Run² + Rise²)

Or use multiplier:
Rafter = Run Γ— Pitch Multiplier

Stair Calculations​

Code Requirements (Typical)​

ElementResidentialCommercial
Max Riser7-3/4"7"
Min Tread10"11"
Min Width36"44"
Min Headroom6'-8"6'-8"

Stair Formula​

Number of Risers = Total Rise Γ· Riser Height
Number of Treads = Risers - 1
Total Run = Number of Treads Γ— Tread Depth

Comfort Formula: Riser + Tread = 17" to 18"

Circle & Arc Calculations​

Circumference = Ο€ Γ— Diameter = 2 Γ— Ο€ Γ— Radius
Diameter = Circumference Γ· Ο€
Radius = Diameter Γ· 2

Ο€ = 3.14159

Arc Length​

Arc Length = (Angle Γ· 360) Γ— Circumference

Pythagorean Theorem​

aΒ² + bΒ² = cΒ²
c = √(a² + b²)

Common Construction Triangles​

BaseHeightDiagonal
345
6810
51213
81517
91215

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 Γ— (1 + Markup%)
Margin:    Selling Price = Cost Γ· (1 - Margin%)
Discount:  Sale Price = Original Γ— (1 - Discount%)

Markup vs Margin​

MarkupMargin
10%9.1%
15%13%
20%16.7%
25%20%
30%23.1%
35%25.9%
40%28.6%
50%33.3%

Temperature​

Β°F = (Β°C Γ— 9/5) + 32
Β°C = (Β°F - 32) Γ— 5/9
Β°FΒ°CSignificance
320Water freezes
404Cold weather concrete limit
5010Many coating minimums
7021Standard curing temp
9032Hot weather concrete
10038Heat stress concern

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