Formulas

Helpful Formulas and Estimating Tips

How to figure coverage factors on any board.

What about cutting waste?

Calculating the Area of a Triangle

Calculating Circles

A secret rule for figuring cedar shingles or shakes.

Roof area by pitch and building size

LINEAR MEASURE

LIQUID MEASURE

Many Other Misc. Calculations

Why re-invent the wheel....try this place.

http://www.unitconversion.org

Nominal divided by Actual (remember NA)

If you learn this, a lot of your figuring problems will be over.

The Nominal size of a board is the way you talk about the size. When talking about a 1x6 board, 1" and 6" is the Nominal size. The actual size is 3/4" x 5-1/2".

The nominal size of a 2x8 is 2" x 8", but the actual size is 1-1/2 x 7-1/2.

To determine accurate coverage, the actual size of the board is used. The actual size is the actual coverage of the board. So for example a 1x6 tongue and groove board gives you an actual coverage value of 5-1/4". It's nominal size is 6" and the actual size is 5-1/4". (It's overall actual size is 5-1/2" but once the togue is in the groove, it actually covers only 5-1/4")

Now apply the formula of Nominal divided by Actual = 6 / 5.25 = 1.14 . This means that you would have to order 14% more of this board to cover what a real 6" board would have covered.

Example

A piece of 1/2 x 6 Cedar Bevel Siding laps over the previous one and leaves an exposure or actual coverage value of 4-1/2". You have to cover 140 sqft using 6" bevel siding. You could easily figure that 6" is 1/2 of a sqft - so right away you know you'll need twice as much or 280 lft of 6" material to cover 140 sqft. But the 6" really isnt 6". When you lap over the next board, you only have a 4-1/2" exposure or actual value. N/A = 6 / 4.5 = 1.333 meaning you have to order 33% more. 280 x 1.333 = 373 lft to order. Add a percentage for cutting waste and you've got it.

This Nominal divided by Actual applies in many places. If you knew that it took 4 bundles of perfection shingles to cover 100 sqft at 5-1/2" exposure and you had to cover 250 sqft, you could easily figure it will take 2.5x4 = 10 bundles. But now if you had to adjust to match a 7" exposure, you would take your 5.5 / 7 = .78 meaning you only need 78% of those 10 bundles, or 8 bundles.

Keep it simple and divide it up by the actual inches.

example..

You have a deck that's 17 feet wide. You'll be using 5/4x6 cedar which actually measures 5-1/2". You'll leave an 1/8" space, so it's actually 5-5/8" of value for each board. 17 feet x 12" = 204 total inches of deck to cover using 5-5/8, you have 204 / 5.625 = 36.27 or 37 boards.

Back

Cutting Waste

There's a general rule of thumb which says to add 5% cutting waste, but this only works in general. It really all depends on the shape you are covering and the materials you are using. If you are covering a triangle and you can only use one side of the board, then you better figure about 1/3 waste or 33%. If you can turn the board over and use the other side as well , then you can cut it down to about 15% waste. If it's a rectangular area of 8' x 20' and your boards are all 8' length, then once you have the correct amount of boards to cover the area, you'll have almost no waste...well you may miss-cut...and there may be a couple of low grade pieces that you don't want to use, so ...forget the percentages and just add a couple of boards. This 5% number that is often used may actually come from the lumber industry's grading rules. Most grades are allowed to be off by 5%.

Back

A secret rule for figuring cedar shingles or shakes.

This was passed down to me from an elderly gentleman who had it passed down to him from an elderly gentleman. Don't ask me why it works, it just does. Although most cedar shingles come in standard size bundles, some shingles such as barn shakes and undercourse still come packaged differently. This method requires you to know the bundle size. A 9/9 pack for example means there are 9 butt ends of the shingle on one side of the bundle, and 9 butt ends of the shingle on the other side. 9/9 packs are pretty standard for 18" and 24" handsplit shakes. Barn shakes which have no taper - straight through 3/8" x18" with no taper is counted only from one side. You never count the same shingle twice. Typical undercourse can be 10/10 packs or 20/20 packs. Perfections are normally 18/18 pack, handsplits are 9/9 pack, white cedar extras are most often 20/20 pack, 24" Royals are 15/15 pack. The rule goes like this.

Add the butt ends of a bundle together (9+9 = 18)

Divide that by '8'. (18/8=2.25)

Multiply the result x the exposure you want to use (2.25 x 8" exposure =18 sq ft) of bundle coverage.

Example

It takes 4 bundles to cover 100 sq ft using 18" perfections @ 5-1/2" exposure.

Perfections are a 18/18 pack - so lets prove it out..

18+18 = 36

36/8 = 4.5

4.5 x 5.5 exposure = 24.75 sqft per bundle.

Close enough to 4 bundles at 100 sqft.

Back

Roof area by pitch and building size

Grab a square, hold it level, sight it along the edge of a roof, and you can pretty accurately determine the pitch of the roof. Using the 12" mark on the base of the square and seeing where the pitched roof crosses the marks on the other side of the square. If the pitch of the roof crosses the 5" mark on the vertical part of the square while being 12" away from the starting point, then you have a 5 pitch roof. Once you know the pitch, you can use the table below to calculate the roofing area to cover by multiplying the corresponding factor from the table below. Look ma no ladder!

Example

You have a building that's 24x32 including overhangs(768 sqft.) You determine the pitch is 4". The factor in the table below for a 4" roof pitch is 1.054. Multiply the building area times the factor - 768 x 1.054 = 809 sqft to cover. Additionally, you would order 10% more for the starter courses, and always round up to the next bundle.

Multiply the sqft area of the building by

3"	1.031	7-1/2"	1.179
3-1/2"	1.042	8"	1.202
4"	1.054	8-1/2"	1.225
4-1/2"	1.068	9"	1.250
5"	1.083	9-1/2"	1.275
5-1/2"	1.10	10"	1.302
6"	1.118	10-1/2"	1.329
6-1/2"	1.137	11"	1.357
7"	1.158	11-1/2"	1.385
		12"	1.414

Back

LINEAR MEASURE

12 inches (in) = 1 foot (ft)

3 feet = 1 yard (yd)

51/2yds = 1 rod (rd), pole, or perch (16-1/2 ft)

40 rods = 1 furlong (fur) = 220 yds = 660ft

8 furlongs = 1 statute mile (mi)

3 land miles = 1 league

5,280 feet = 1 statute or land mile

6,076.11549 ft = 1 international nautical mile

LIQUID MEASURE

When necessary to distinguish the liquid pint or quart from the dry pint or quart, the word "liquid" or the abbreviation "Iiq" should be used in combination with the name or abbreviation of the liquid unit

4 gills (gi) = 1 pint (pt) = 28.875 cu in

2 pints = 1 quart (qt) = 57.75 cu in

4 quarts = 1 gallon (gal) = 231 cu in

DRY MEASURE

When necessary to distinguish the dry pint or quart from the liquid pint or quart, the word "dry" should be used in combination with the name or abbreviation of the dry unit

2 pints = 1 qt = 672006 cu in

8 quarts = 1 peck = 537605 cu in

4 pecks = 1 bushel (bu) =2,150.42 cu in

CIRCULAR MEASURE

Second (") = 1/60 minute

Minute (') = 60 seconds

Degree (o) = 60 minutes

Right angle = 90 degrees

Straight angle = 180 degrees

Circle = 360 degrees

TROY WEIGHT

24 grains = 1 pennyweight (dwt)

20 pennyweights = 1 ounce troy (oz t)

12 ounces troy = 1 pound troy (Ib t)

APOTHECARIES' WEIGHT

20 grains = 1 scruple (s ap)

3 scruples = 1 dram apothecaries' (dr ap)

8 drams apoth. = 1 ounce apothecaries' (oz ap)

12 oz. Apoth. = 1 pound apothecaries' (lb ap)

AREA MEASURE

144 square inches = 1 sq ft

9 square feet = 1 sq yd = 1296 sq in

30-1/4 square yards = 1 sq rd = 272-1/4 sqft

160 sq rods = 1 acre = 4840 sq yards

640 acres = 1 sq mi

1 mile square = 1 section (of land)

6 miles square = 1 township = 36 sections

CUBIC MEASURE

1728 cubic inches = 1 cubic foot

27 cubic feet = 1 cubic yd

APOTHECARIES' FLUID MEASURE

60 minims (min) = 1 fl dram (fl dr)

8 fluid drams = 1 fl ounce (fl oz)

16 fluid ounces = 1 pt

2 pints = 1 qt

4 quarts = 1 gallon

AVOIRDUPOIS WEIGHT

When necessary to distinguish the avoirdupois dram from the apothecaries' dram, or to distinguish the avoirdupois dram or ounce from the fluid dram or ounce, or to distinguish the avoirdupois ounce or pound from the troy or apothecaries' ounce or pound, the word "avoirdupois" or the abbreviation "avdp" should be used in combination with the name or abbreviation of the avoirdupois unit (The word "grain" is the same in all three weights.)

27-11/32 grains = 1 dram (dr)

16 drams = 1 ounce = 437-1/2 grains

16 ounces = 1 Ib = 256 drams

100 pounds = 1 hundredweight (cwt)*

20 hundredweights = 1 ton = 2000 Ibs*

In gross/long measure the following values are recognized.

112 pounds = 1 gross/long (cwt)*

20 hundredweight = 1 gross/long ton

*When the terms "hundredweight" and "ton" are used unmodified, they are commonly understood to be the 100 pound hundredweight, and the 2,000 pound ton, respectively; these units may be designated "net" or "short" when necessary to distinguish them from the corresponding units in gross or long measure.

METRIC LINEAR MEASURE

10 millimeters = 1 centimeter (cm)

10 centimeters = 1 decimeter (dm)

10 decimeters = 1 meter (m)

10 meters = 1 dekameter (dam)

10 dekameters = 1 hectometer (hm)

10 hectometers = 1 kilometer (km)

METRIC WEIGHT MEASURE

10 milligrams = 1 centigram (yd)cm)

10 centigrams = 1 decigram (dm)

10 decigrams = 1 gram (m)

10 gram = 1 dekagram (dam)

10 dekagrams = 1 hectogram (hm)

10 hectograms = 1 kilogram (km)

1000 kilograms = 1 metric ton (yd)t)

METRIC AREA MEASURE

100 square mm = 1 sq centimeter (cm2)

10,000 square cm = 1 sq meter (m2)

100 square meters = 1 are (a)

100 ares = 1 hectare (ha)

100 hectares = 1 sq kilometer (km2)

METRIC VOLUME MEASURE

10 milliliters = 1 centiliter (cl)

10 centiliters = 1 deciliter (dl)

10 deciliters =1Iiter(l)

10 liters = 1 dekaliter (dal)

10 dekaliters = 1 hectoliter (hl)

10 hectoliters = 1 kiloliter (kl)

METRIC CUBIC MEASURE

1,000 cubic mm = 1 cu centimeter (cm3)

1,000 cm3 = 1 cu decimeter (dm3)

1 ,000 dm' = 1 cu meter (m3)

LENGTH

1 angstrom' =0.1millimicron

(light wave measurement)

=0.0001 micron

=0.0000001 mm

=0.000000004 in

1 cable's length = 120 fathoms

=720 feet

=219.456 meters

1 centimeter =0.3937 in

1 chain = 66 feet

(Gunter's surveyor's) =20.1168 meters

1 decimeter = 3.937 inches

1 dekameter = 32.808 feet

1 fathom = 6 feet

=1.8288 meters

1 foot = 0.3048 meter

1 furlong = 10 chains (surveyors)

=660 feet

=220 yards

=1/2 a statute mile

=201.168 meters

1 inch = 2.54 centimeters

1 kilometer = 0.621 mile

1 league (land)= 3 statute miles

=4.828 kilometers

1 link = 7.92 inches

(Gunter's or survyor's) =0.201168 meter

1 meter = 39.37 inches

=1.094 yards

1 micron = 0.001 millimeter

=0.00003937 inch

1 mil =0.001 inch

=0.0254 millimeter

1 mile = 5,280 feet

(statute or land)=1.609 kilometers

1 mile = 1.852 kilometers

(nautical international) =1.151 statute miles

=0.999 US Nautical

1 millimeter =0.03937 inch

1 millimicron =0.001 micron

=0.00000003937 in

1 nanometer = 0.001 micrometer

=0.00000003937 in

1 point (typography) = 0.013837 inch

=1/72 inch

=0.351 millimeter

1 rod/pole/perch = 16-1/2 feet

=5.0292 meters

1 yard = 0.9144 meter

CAPACITIES OR VOLUMES

1 barrell, liquid = 31 to 42 gallons

1 barrell (standard for fruits/vegetables/dry commodities, not cranberries)

= 7,056 cubic inches

=105 dry quarts

=3.281 bushels

1 barrell (cranberries)= 5.286 cubic inches

=86-45/64 dry quarts

=2.709 bushels, struck

1 bushel, struck =2,150.42 cu inches

=35.238 liters

1 bushel, heaped= 2,747.715 cu inches

=1.278 bushels, struck

1 cord (firewood) = 128 cubic feet

1 cubic centimeter = .061 cubic inches

1 cubic decimeter = 61.024 cubic inches

1 cubic foot = 7.481 gallons

= 28.316 dm

1 cubic inch = 0.554 fluid ounce

=4.433 fluid drams

=16.387 cm

1 cubic meter =1.308 cubic yards

1 cubic yard = 0.765 cubic meter

1 cup (measuring) = 8 fluid ounces

=1/2 liquid pint

1 dram (fluid or liquid us) = 1/8 fluid ounce

=0.226 cubic inch

=3.697 milliliters

=1.041 British drachms

1 dekaliter = 2.642 gallons

=1.135 pecks

1 gallon US =231 cubic inches

=3.785 liters

=0833 British gallon

=128 US fluid ounces

1 gallon British = 277.42 cubic inches

=1.201 US gallons

=4.546 liters

=160 British fl ounces

1 gill = 7.219 cubic ounces

=4 fluid ounces

=0.118 liter

1 hectoliter = 26.418 gallons 2.838 bushels

1 liter = 1.057 liquid quarts

=0.908 dry quart

=61.024 cubic inches

1 milliliter =0.271 fluid dram

=16.231 minims

=0.061 cubic inch

1 ounce = 1.805 cubic inch

(fluid or liquid us) =29.574 milliliters

=1.047 British ounces

1 peck = 8.810 liters

1 dry pint = 33.600 cubic inches

=0.551 liter

1 liquid pint = 28.875 cubic inches

=0.473 liter

1 dry quart US = 67.201 cubic inches

=1.101 liters

=0.969 British quart

1 liquid quart US = 57.75 cubic inches

=0.946 liter

1 assay ton4 = 29.167 grams

1 carat =200 milligrams

=3.086 grains

1 dram apothocaries' = 60 grains

=3.888 grams

1 dram, acoirdupois = 27.344 grains

=1.772 grams

1 grain =64.79891 milligrams

1 gram = 15.432 grains

=0.035 ounce avdp

1 hundredweight (gross or long) = 112 pounds

=50.802 kilograms

1 hundredweight (net or short) = 100 pounds

=45.359 kilograms

1 kilogram =2.205 pounds

1 microgram = 0.000001 gram

1 milligram =0.015 grain

1 ounce avdp = 437.5 grains

=0.911 troy/apoth oz

=28.350 grams

1 oz troy/apoth = 480 grains

=1.097 avdp oz

=31.103 grams

1 pennyweight = 1.555 grams

1 point = 0.01 carat

=2 milligrams

1 avdp pound = 7000 grains

=1.215 troy/apoth Ibs

=453.59237 grams

1 Ib troy/apoth = 5,760 grains

=0.823 avdp Ib

=373.242 grams

1 ton = 2,240 lbs

(gross or long)' =1.12 net tons

=1.016 metric tons

1 metric ton = 2,204.623 Ibs

=0.984 gross ton

=1.102 net tons

1 ton (gross or long) =2000 lbs

=0.893 gross ton

=0.907 metric ton

AREAS or SURFACES

1 acre = 43,560 square ft

=4,804 square yds

=0.405 hectare

1 are = 119.599 square yds 0.025 acre

1 hectare = 2.471 acres

1 square cm = 0.155 square inch

1 square dm = 15.5 square inches

1 square foot = 929.030 sq cm

1 square inch = 6.4516 sq cm

1 square km = 0.386 sq mile 247.105 acres

1 square meter = 1.196 sq yds 10.764 sq feet

1 square mile =258.999 hectares

1 square mm =0.002 square inch

1 square yard = 0.836 square meters

Customery/Metric Conversions

Inch (in) x 25.4 = millimeter

Foot (ft) x .3 = meter

Yard (yd) x .9 = meter

Mile (mi) x 1.6 = kilometer

Square inch x 6.5 = sq centimeter

Square foot x .1 = sq meter

Square yard x .8 = sq meter

Acre x .4 = hectare

Cubic foot x .03 = cu meter

Millimeter (mm) x .04 = inch

Meter (m) x 3.3 = foot

Meter (m) x 1.1 = yard

Kilometer (km) x .6 = mile

Sq Centimeter (cm') x .2 = sq inch

Sq meter (m') x 10.8 = sq feet

Sq meter (m') x 1.2 = sq yard

Hectare (ha) x 2.5 = acre

Cu meter (m') x 35.3 = cu foot

Units of Length and Area

Inch (in) = 25.4 millimeters

Foot (ft) = 12 in = .305 meter

Yard (yd) = 36 in or 3 ft = .914 meter

Mile (mi) = 5,280 ft = 1.609 kilometers

Square inch (in') = 6.452 cm'

Square foot (ft') = 144 sq in =.093 m'

Millimeter (mm) = .001 meter = .039 inch

Centimeter (cm) = .01 meter = .394 inch

Decimeter (dm) = .1 meter = 3.937 inches

Meter (m) = 3.281 feet

Kilometer (km) = 1,000 m = .621 mile

Sq millimeter (mm2) = .000001 m2 = .002 sq in

Sq centimeter (cm2) = .0001 m2 = .155 sq in

Sq decimeter (dm2) = .01 m' = 15.5 sq in

Sq meter (M2) = 10.764 sq ft

Hectare (ha) = 10,000 sq meters = 2.471 acres

Sq kilometer (km2) = 1,000,000 sq meters = .386 sq miles

Units of Weight (or Mass)

Grain = .065 gram

Ounce (oz avdp) = 437.5 grains = 28.350 grams or 16 drams

Pound (lb avdp) = 7,000 grains = .454 kilogram or 16 ounces

Hundredweight (cwt) = 100 pounds = 45.359 kg

Ton, short (tn) = 2,000 pounds = .907 metric ton

Ton, long = 2,240 pounds = 1.016 metric tons Troy*

Ounce (oz troy)* = 480 grains = 31.104 grams

Pound (lb troy) = 5,760 grains = .373 kilograms

Gram (g) = .035 oz avdp or .032 oz troy

Dekagram (dag) = 10 g = .353 oz avdp or .322 oz troy

Kectogram (hg) = 10 g = 3.527 oz avdp or 3.215 oz troy

Kilogram (kg) = 1000 g = 2205 lbs avdp - or - 2.679 lbs troy

Metric Ton = 1000 kilograms

Units of capacity (liquid)

Fluid Ounce (fl oz) = 29.573 ml

Pint (pt) = 16 fl oz = .473 liter

Quart (qt) = 32 fl oz or 2 pt = .946 liter

Gallon (gal) = 8 pt or 4 qt = 3.785 liters

Milliliter (ml) = .001 liter = .034 fl oz

Liter (I) = 1.057 qt

Units of capacity (dry)

Pint (pt) = .551 dm*3

Quart (qt) = 2 pints = 1.101 dm*3

Peck (pk) = 8 quarts = 8.810 dm*3

Milliliter (ml) = .001 liter = .002 pt

Liter (D = .908 qt

Hectoliter (hl) = 100 liters = 2.838 qt

Geometric Formulas

CIRCLE

area = 1/2 diameter x 1/2 circumference

area of sector = length of arc x 1/2 radius

area of segment which is greater than semicircle = area of sector of equal radius + area of the triangle

area of segment which is less than semicircle = area of sector of equal radius - area of the triangle

circumference = diameter x 3.1416

= radius x 6.283185

diameter = circumference x .3183

radius = cirumference x .0159155

CYLINDER OR PRISM

surface = (area of both ends) + (length x circumference)

ELLIPSE

area = product of the two diameters x .7854

PARABOLA

area = 2/3 altitude x base

PARALLELOGRAM

area = altitude x base

POLYGON REGULAR)

area = sum of sides x perpendicular from center to one of sides divided by 2

PYRAMID OR CONE

surface = circumference of base x 1/2 slant height + area of base

contents = 1/2 altitude x area of the base

RECTANGLE

area = length x width

SPHERE

circumference = cube root of solidity x 3.8978

= square root of surface x 1.772454

contents = diameter x .5236

contents of segment = (height squared + 3 times the square of the radius of the base) x (height x .5236)

diameter = square root of surface x .56419

= cube root of solidity x 1.2407

surface = circumference x diameter

volume = surface x 1/6 diameter

= diameter cubed x .5236

= radius cubed x 4.1888

= circumference cubed x .016887

SQUARE

area = length x width

TRAPEZIUM

area = divide trapezium into two triangles; add the areas

TRAPEZOID

area = altitude x 1/2 sum of parallel sides

TRIANGLE

area = 1/2 altitude x base

WEDGE

contents = 1/2 altitude x area of base