01
Know Your Dimensions + Slope + Circles
The Three Dimensions
1D — Length
One measurement. Trim, base, fascia.
2D — Area
Area = Length × Width
3D — Volume
Volume = L × W × H
Circles
Diameter
D = 2r
Circumference
C = π × D = 2πr (π≈3.1416)
Area
A = πr² shortcut: A ≈ 0.785 × D²
Slope & Right Triangles
Pythagoras
a² + b² = c²
Slope
Slope = Rise ÷ Run
3-4-5 Square Check
a²+b²=c² → 9+16=25
If legs are 3 & 4, the diagonal must be exactly 5 for square. Use any multiple: 6-8-10, 9-12-15.
02
Shapes, Conversions & Field Tricks
Common Shapes — Area & Volume
Square
A = s²
Rectangle
A = L × W
Triangle
A = (b × h) ÷ 2
Trapezoid
A = (a+b)/2 × h
Parallelogram
A = b × h
Box / Cube
V = L × W × H
Cylinder Vol
V = πr² × h
Cylinder Side
A = 2πr × h
Field tip: for odd shapes, break into rectangles + triangles, add them. Faster than hunting a perfect formula.
Inches → Feet (Decimal)
| Inches | Decimal Ft | Formula |
|---|---|---|
| 1" | 0.083' | |
| 2" | 0.167' | Feet = In ÷ 12 |
| 3" | 0.250' | |
| 4" | 0.333' | Ex: 7" = 0.583' |
| 6" | 0.500' | |
| 9" | 0.750' | |
| 12" | 1.000' |
Handy Ruler — No Tape?
Thumb → Index: ~6"
Palm Width: ~4"
Hand Span: ~9"
Forearm: ~18"
Measure your own hand once, write it on your tape. Good enough for quick estimates.
Temperature Math
C = (F − 32) × 5/9
F = C × 9/5 + 32
Example: 68°F = 20°C
Freezing: 32°F = 0°C Comfort: 72°F ≈ 22°C
All decimals here use US standard. Divide inches by 12 on any calculator — no table needed in the field.
03
Common Trade Units & Flooring Math
Trade Coverage — How We Count
Paint: one gallon rolls ~350-400 sq ft per coat. Porous or textured drops to ~250-300.
Wallpaper: single roll ≈ 28 sq ft, double roll ≈ 56 sq ft. Match repeat eats 15-20%.
Tile: tiles needed = floor sq ft ÷ tile area. Add 10-15% waste, 18-20% for diagonal.
Carpet: sq yd = sq ft ÷ 9. Seamed broadloom needs extra for pattern and fill.
Concrete: cu ft = L × W × Thick(ft). Cu yd = cu ft ÷ 27. Order +5% for uneven grade.
Roofing: 1 square = 100 sq ft. Bundles per square vary (3-bund typical). Check ridge and starter.
Drywall / Sheathing: sheet 4×8 = 32 sq ft. Sheets = total area ÷ 32. Subtract only large openings >32 sf.
Board Feet — Lumber Logic
BF = (T" × W" × L') ÷ 12
Thickness in inches × width in inches × length in feet, divided by 12. One board foot = 144 cu in — a 1"×12"×12" block.
Ex: 2×6×10' → (2×6×10)/12 = 10 BF
Quarter sizes: 4/4=1", 5/4=1.25", 8/4=2"
Stair Math — Quick Layout
Number of risers = Total Rise ÷ Target Riser Height
Round to a whole count per comfort and code. Round risers, then: Exact Riser = Total Rise ÷ Count.
Run per tread = 10" to 11" (plus nosing). One less tread than risers if top is landing.
Quick Conversions On Site
Linear Feet: total length. Trim, base, fascia — just add runs.
Sq Ft → Sheets: Sheets = Area ÷ 32 (4×8). ÷ 48 for 4×12.
Board Foot: 1 BF = 144 cubic inches. Not linear, not square.
FIELD CHECK
Before you order: add waste, check bundle counts, confirm actual sheet size (some 4×9, 4×10). Measure twice, convert once.
Before you order: add waste, check bundle counts, confirm actual sheet size (some 4×9, 4×10). Measure twice, convert once.
04
Business Math for the Jobsite
Markup vs Margin — Don’t Confuse Them
Markup lives on cost. You add it:
Price = Cost × (1 + Markup%)
Margin lives on price. It’s what you keep:
Margin% = (Price − Cost) ÷ Price
Example: $100 cost + 30% markup = $130 price = 23.1% margin
To get 30% margin, you need 42.86% markup. Margin always looks smaller than markup for same dollars.
To get 30% margin, you need 42.86% markup. Margin always looks smaller than markup for same dollars.
Percent Math You Actually Use
X% of N = N × (X÷100)
15% of 240 = 240×0.15 = 36
Add X%: N × (1 + X/100)
Remove X%: N × (1 − X/100)
What To Charge Per Hour
Break-Even $/hr = (Annual Overhead + Profit Goal) ÷ Billable Hrs
Overhead = rent, insurance, trucks, phones, non-billable time. Billable hrs = hours you can actually invoice (often 1,000-1,400/yr per person, not 2,080).
Ex: $85k overhead + $40k profit = $125k ÷ 1,200 hrs ≈ $104/hr
Waste Factors — Add Before You Buy
| Material / Layout | Add |
|---|---|
| Hardwood straight | 8-10% |
| Hardwood diag / wide plank | 12-15% |
| Tile straight | 12-15% |
| Tile diagonal / large format | 15-20% |
| Carpet broadloom | 5-7% |
| Sheet vinyl | 3-5% |
| Roofing (cut, valley, hips) | 7-12% |
| Lumber framing | 10-15% |
Pattern match, out-of-square walls, and small rooms burn more waste. When in doubt, round up one bundle/box.
Land & Volume Constants
1 Acre: 43,560 sq ft ≈ 208.7' × 208.7' ≈ 4,840 sq yd
Board Foot: 144 cu in
Cubic Yard: 27 cu ft (3'×3'×3')
Closing Note From The Field
“Math doesn’t make the job easier — it makes the mistakes smaller. Measure in the unit you’ll order in. Write your waste on the takeoff, not in your head.”
Go Deeper: The Sovereign Trades Math Library
Every formula on these cards is taught in full — with worked jobsite problems — in three GSU books. Each is free to read cover-to-cover on the GSU website, with a free audiobook resource that reads it aloud. Kindle editions are $3.99 on Amazon.
Trades Algebra
The equations behind estimates, conversions, and every “solve for X” moment on a job.
Read Free →Trades Geometry
Squares, slopes, circles, and layout — the geometry that keeps buildings true.
Read Free →Trades Business Math
Markup, margin, overhead, and what to charge — the numbers that keep a shop alive.
Read Free →Frequently Asked Questions
What is Contractor’s Field Math?
It is a free four-card jobsite math reference from Global Sovereign University, designed to print on standard 8.5×11 paper and ride in a truck, toolbox, or clipboard. Card 1 covers dimensions, slope, right triangles, and circles. Card 2 covers common shapes, inch-to-decimal-foot conversion, and field tricks. Card 3 covers trade coverage rates, flooring math, stair layout, and board feet. Card 4 covers the business math of markup, margin, hourly rates, and waste factors.
What is the 3-4-5 rule and why do contractors use it?
The 3-4-5 rule is a field application of the Pythagorean theorem (a² + b² = c²). Measure 3 feet along one edge and 4 feet along the other; if the corner is truly square, the diagonal between those marks must be exactly 5 feet, because 9 + 16 = 25. Any multiple works the same way — 6-8-10, 9-12-15 — which is useful for laying out larger walls, decks, and foundations without a framing square.
What is the difference between markup and margin?
Markup lives on cost: Price = Cost × (1 + Markup%). Margin lives on price: Margin% = (Price − Cost) ÷ Price. They are not the same number. A $100 cost with 30% markup produces a $130 price, but that job carries only a 23.1% margin. To actually keep a 30% margin you need a 42.86% markup. Confusing the two is one of the most common ways small contractors underprice their work.
How do I figure out what to charge per hour?
Break-Even $/hr = (Annual Overhead + Profit Goal) ÷ Billable Hours. Overhead includes rent, insurance, trucks, phones, and all non-billable time. Billable hours are the hours you can actually invoice — often only 1,000-1,400 per year per person, not the 2,080 hours in a full work year. Example: $85k overhead plus a $40k profit goal is $125k; divided by 1,200 billable hours, that’s roughly $104/hr just to break even and hit the goal.
How much waste should I add when ordering materials?
It depends on the material and the layout. Typical add-ons: hardwood straight 8-10%, hardwood diagonal or wide plank 12-15%, tile straight 12-15%, tile diagonal or large format 15-20%, carpet broadloom 5-7%, sheet vinyl 3-5%, roofing with cuts, valleys, and hips 7-12%, and lumber framing 10-15%. Pattern match, out-of-square walls, and small rooms all burn extra material — when in doubt, round up one bundle or box.
Is this reference really free, and can GENO help me with the math?
Yes. This page and its printable cards are completely free, like every learning resource at Global Sovereign University, a 501(c)(3) nonprofit whose sole income is book sales — Pupils before Profits. The formulas here pair directly with three GSU Sovereign Trades books: Trades Algebra, Trades Geometry, and Trades Business Math, each free to read in full on the GSU website with a $3.99 Kindle edition on Amazon. And yes — GENO, GSU’s free adaptive AI tutor, can walk you through any of this math in any of 83 languages, 24/7. A robot you can actually TALK to.
Stuck on a takeoff? GENO — GSU’s free AI tutor, available 24/7, a robot you can actually TALK to — can walk you through any formula on this page in any of 83 languages. Find him in the footer of Global Sovereign University pages.