Common Unit Conversions + Math Formulas

Why this matters

Field math constant. Customer asks "what's that in pounds?" - quick mental conversion shows expertise. Calculating area for pricing, volume for materials, temperature for adjustments, weight for capacity - every trade needs the basics. This is the field card.

Length + area + volume

Length: 1" = 25.4 mm = 2.54 cm; 1 ft = 12" = 304.8 mm; 1 yd = 3 ft = 36"; 1 mi = 5,280 ft = 1.609 km; 1 m = 39.37" = 3.28 ft; 1 km = 0.62 mi. Pre-calc: 8 ft = 96"; 10 ft = 120"; 12 ft = 144"; 16 ft = 192"; 25 ft = 300".

Area: 1 sq ft = 144 sq in; 1 sq yd = 9 sq ft; 1 acre = 43,560 sq ft = 4,840 sq yd; 1 sq m = 10.76 sq ft; 4×8 sheet = 32 sq ft; 4×10 sheet = 40 sq ft. Formulas: rectangle L×W; triangle 1/2 × B × H; circle π × r²; trapezoid 1/2 × (B1 + B2) × H.

Volume: 1 cu ft = 1,728 cu in = 7.48 gal; 1 cu yd = 27 cu ft = 202 gal; 1 gal = 0.134 cu ft = 3.785 L; 1 L = 0.264 gal; 1 cu m = 35.3 cu ft. Formulas: box L×W×H; cylinder π × r² × H; cone 1/3 × π × r² × H.

Weight

1 lb = 16 oz = 453.6 g; 1 ton (US) = 2,000 lb; 1 kg = 2.205 lb; 1 cu ft water = 62.4 lb = 7.48 gal; 1 gal water = 8.34 lb; 1 cu yd concrete = 4,050 lb. Material density (lbs/cu ft): concrete 150; steel 490; aluminum 168; copper 559; lumber dry 30 - 50; drywall 1/2" 1.6 lbs/sq ft.

Temperature

Fahrenheit ↔ Celsius:

• °F to °C: (°F - 32) × 5/9
• °C to °F: (°C × 9/5) + 32

Quick references:

• 32°F = 0°C (freezing)
• 50°F = 10°C
• 68°F = 20°C (room temp)
• 72°F = 22°C
• 86°F = 30°C
• 100°F = 38°C
• 212°F = 100°C (boiling)

Conversion shortcuts (rough):

• °C to °F: double + 30 (approximation)
• 20°C ≈ 70°F
• 30°C ≈ 86°F (closer to 90 in shortcut)

Pressure

• 1 PSI = 6.895 kPa
• 1 PSI = 2.04 inches of mercury (inHg)
• 1 PSI = 27.7 inches of water column (" WC)
• 1 atmosphere = 14.7 PSI = 760 mmHg
• 1 bar = 14.5 PSI

HVAC + plumbing:

• 1 ft head of water = 0.434 PSI
• 1 PSI = 2.31 ft head of water

Flow rate

• 1 GPM = 0.063 L/s
• 1 GPM = 3.78 L/min
• 1 CFM = 0.47 L/s
• 1 CFM = 1.7 m³/hr

Energy / power

1 W = 3.412 BTU/hr; 1 kW = 3,412 BTU/hr; 1 HP = 745.7 W = 2,545 BTU/hr; 1 BTU = 0.293 Wh; 1 ton refrigeration = 12,000 BTU/hr = 3,517 W; 1 kWh = 3,412 BTU; 1 therm = 100,000 BTU. Heating: 1 gal #2 oil = 138,500 BTU; 1 cu ft NG = 1,000 BTU; 1 lb propane = 21,500 BTU; 1 gal propane = 91,500 BTU; 1 cord wood ~20M BTU (species-dependent).

Time

60 sec = 1 min; 60 min = 1 hr; 24 hr = 1 day; 168 hr = 1 week; 720 hr = 30 days; 8,760 hr = 1 year. Decimal time: 0.25 hr = 15 min; 0.5 hr = 30 min; 0.75 hr = 45 min; 0.1 hr = 6 min; 0.01 hr ≈ 36 sec.

Angles

• 1 degree = 60 minutes = 3,600 seconds
• 90° = quarter circle (right angle)
• 180° = half circle (straight line)
• 360° = full circle
• 1 radian = 57.3°

Common roof + framing angles:

• 4/12 pitch: 18.43° slope
• 6/12 pitch: 26.57°
• 8/12 pitch: 33.69°
• 12/12 pitch: 45°
• 14/12 pitch: 49.40°

Roof pitch

• 4/12 (4 in rise per 12 in run): 33% grade
• 6/12: 50% grade
• 8/12: 67% grade
• 12/12: 100% grade (45°)
• "Steep" = above 8/12

Common job-site calculations

Slab volume (4" × 10' × 12'): 10 × 12 × (4/12) = 40 cu ft; 40 / 27 = 1.48 cu yd. Floor area irregular room: divide into rectangles + triangles, sum. Wall paint (12 × 14 × 8 ft): perimeter 52 ft × 8 ft = 416 sq ft − openings ~ 360 sq ft net = 1 gallon for one coat. Trim for 12 × 14 room: perimeter 52 ft + 10% waste = 57 ft baseboard. 2x4 studs 16" OC for 14 ft wall: 14 / 1.33 = 10.5 + corners = 12 studs + plates = 28 LF.

Trench: L × W × D = cu ft, ÷ 27 = cu yds. 50 × 1 × 2 = 100 cu ft = 3.7 cu yds. Cylindrical hole (fence post 8" × 3 ft): π × 0.167² × 3 = 0.26 cu ft.

Materials estimation: carpet × 1.1 (10% waste); wallpaper single roll covers ~36 sq ft + 10 - 15% for matching; roofing 1 square = 100 sq ft + 10 - 15% waste/ridge/valleys; drywall 4 × 8 sheet = 32 sq ft + 10 - 15% waste; insulation per manufacturer + 10% waste.

Money math

Markup vs margin:

• Markup ≠ margin (common confusion)

Common percentages:

• 5% = 0.05 = 1/20
• 10% = 0.10 = 1/10
• 15% = 0.15 = 3/20
• 25% = 0.25 = 1/4
• 33.3% = 1/3
• 50% = 1/2

Sales tax calculations (varies by state):

• Most US: 5 - 10%
• Add to subtotal

Common math mistakes

Markup vs margin confusion (50% markup is 33% margin). Linear vs square (100 sq ft of carpet ≠ 100 ft of carpet). Cubic confusion. Decimal feet ≠ feet + inches (3.4 ft = 3 ft 4.8 in, NOT 3 ft 4 in). Rounding errors. Forgetting waste factor (10% on most materials).

References

• NIST measurement standards
• Industry-specific design calculations
• "Pocket Ref" by Thomas J. Glover (industry reference)
• Manuall internal: Fastener Torque Reference, Tape Measure + Fractions