Formulas for Measure & Volume http://formulas.blog.com Wed, 23 Feb 2005 14:37:55 +0000 http://wordpress.org/?v=2.7 en hourly 1 Handy Formulas http://formulas.blog.com/2005/02/23/handy-formulas/ http://formulas.blog.com/2005/02/23/handy-formulas/#comments Wed, 23 Feb 2005 14:37:55 +0000 kontikiman  "Never memorize anything you can read out of a book." --Albert Einstein

Here are many handy formulas for those of us who take Einstein far too seriously.
At least, that's my excuse for never memorizing most of the following.

Terminology:

p the symbol for its ratio [ p = circumference ¸ diameter ] It is represented as 3.1416.

¸ operation, divide

´ , · operation, multiply

Ö square root

a = area, a measure of the size of its surface. Areas are measured in square units.

b = breadth of base.

h = perpendicular height.

l = length of base.

p = perimeter of a plane figure is the distance around its edge or boundary. This is measured in linear units.

r = length of radius.

t = length of top.

v = volume of a solid figure is a measure of the amount of space it occupies. This is measured in cubic units. 

 

 

Formulas  for Perimeters

Circle

p = 2 ´ p ´ r
p = p ´ d

Rectangle

p = 2 ( b + h )

 

Formulas  for Area

Circle

a = p ´ r2

Rectangle, Parallelogram

a = b ´ h

Triangle

a = ½ ´ b ´ h

Trapezium

a = ((a + b) h) / 2

Cube (or cubelike object)

a = h ´ b ´ 6

Prism

a = (b ´ h) + (3 ´ l ´ b)

Cylinder

a = (2 ´ p ´ r ´ l) + (2 ´ p ´ r2)

Pyramid

a = (2 ´ b ´ h) + (b2)

Sphere

a = 4 ´ p ´ r2

 

 

 

 

Formulas  for Volume

Cone

v = (p ´ r2 ´ h) / 3

Cube or cubelike object

v = b ´ h ´ l

Cylinder

v = p ´ r2 ´ l

Prism

v = (b ´ h ´ l) / 2

Pyramid

v = (b ´ h ´ l) / 3

Sphere

v = (4 ´ p ´ r3) / 3

 

Units of Measure

Decimal Equivalents

Oz.

LB

1

0.0625

2

0.125

3

0.1875

4

0.25

5

0.3125

6

0.375

7

0.4375

8

0.5

9

0.5625

10

0.625

11

0.6875

12

0.75

13

0.8125

14

0.875

15

0.9375

 

In.

ft.

1

0.0833

2

0.1667

3

0.2500

4

0.3333

5

0.4167

6

0.5000

7

0.5833

8

0.6667

9

0.7500

10

0.8333

11

0.9167

 

 

Avoirdupois
16 dr. make 1 oz.
16 oz. make 1 lb.
14lb make 1 stone
28lb make 1 qr.
4 qrs. make 1 cwt.
20 cwt. make 1 ton

Apothecaries
20gr. make 1 scru.
3 scr. make 1 dram
3 dr. make 1 ounce
12 oz. make 1 pound

Troy
24 gr. make 1dwt.
20 dwt. make 1 oz.
12 oz. make 1 lb.

Solid (or cubic)
1728 cu.in. in 1 cu. ft.
27 cu. ft. in 1 cu. yd.

Paper
24 sheets make 1 quire
20 quires make 1 ream

 

 Time
60 seconds make 1 minute
60 minutes makes 1 hour
24 houres make 1 day
7 days make 1 week
4 weeks make 1 month
52 weeks make 1 year

 

Long Measure
2 barley corns make 1 inch
12 inches make 1 foot
3 feet make 1 yard
6 feet make 1 fathom
5½ yards make 1 pole
40 poles make 1 furlong
8 furlongs make 1 mile
3 miles make 1 league
69½ miles make 1 degree

Coal Measure
3 bushels make 1 sack
36 bushels make 1 chaldron

Cloth Measure
2¼ inches make 1 nail
4 nails make 1 quarter
3 quarters make 1 Fl. ell
4 quarters make 1 yard
5 quarters make 1 En. el
6 quarters make 1 Er. el

Dry Measure
2 gallons make 1 peck
4 pecks make 1 bushel
4 bushel make 1 sack
8 bushels make 1 quarter
4 quarters make 1 chaldron
10 quarters make 1 last.

Wine Measure
2 pints make 1 quart
4 quarts make 1 gallon
10 gallons make 1anchor
42 gallons make 1 tierce
63 gallons make 1 hogshead
12 hogsheads make 1 pipe
2 pipes make 1 tun

Ale and Beer
2 pints make 1 quart
4 quarts make 1 gallon
9 gallons make 1 firkin
2 firkins make 1 kilder
2 kilderkins make 1 barrel
1½ barrels make 1 hogshead
2 barrels make 1 punch
3 barrels make 1 butt

Land Measure
9 feet make 1 yard
30¼ yards make 1 pole
40 poles make 1 rod
4 rods make 1 acre

 

 Conversions

Linear Conversions

Converting Inches & Centimeters

Units

Approx

Accurate

in ® cm

´ 2.5

´ 2.54

cm ® in

¸ 2.5

¸ 2.54

 

Converting Feet & Meters

Units

Approx

Accurate

fr ® m

´ 2.5

´ 2.54

m ® ft

¸ 2.5

¸ 2.54

 

Converting Yards & Meters

Units

Approx]]>


 “Never memorize anything you can read out of a book.” –Albert Einstein

Here are many handy formulas for those of us who take Einstein far too seriously.
At least, that’s my excuse for never memorizing most of the following.

Terminology:

p the symbol for its ratio [ p = circumference ¸ diameter ] It is represented as 3.1416.

¸ operation, divide

´ , · operation, multiply

Ö square root

a = area, a measure of the size of its surface. Areas are measured in square units.

b = breadth of base.

h = perpendicular height.

l = length of base.

p = perimeter of a plane figure is the distance around its edge or boundary. This is measured in linear units.

r = length of radius.

t = length of top.

v = volume of a solid figure is a measure of the amount of space it occupies. This is measured in cubic units. 

 

 

Formulas  for Perimeters

Circle

p = 2 ´ p ´ r
p = p ´ d

Rectangle

p = 2 ( b + h )

 

Formulas  for Area

Circle

a = p ´ r2

Rectangle, Parallelogram

a = b ´ h

Triangle

a = ½ ´ b ´ h

Trapezium

a = ((a + b) h) / 2

Cube (or cubelike object)

a = h ´ b ´ 6

Prism

a = (b ´ h) + (3 ´ l ´ b)

Cylinder

a = (2 ´ p ´ r ´ l) + (2 ´ p ´ r2)

Pyramid

a = (2 ´ b ´ h) + (b2)

Sphere

a = 4 ´ p ´ r2

 

 

 

 

Formulas  for Volume

Cone

v = (p ´ r2 ´ h) / 3

Cube or cubelike object

v = b ´ h ´ l

Cylinder

v = p ´ r2 ´ l

Prism

v = (b ´ h ´ l) / 2

Pyramid

v = (b ´ h ´ l) / 3

Sphere

v = (4 ´ p ´ r3) / 3

 

Units of Measure

Decimal Equivalents

Oz.

LB

1

0.0625

2

0.125

3

0.1875

4

0.25

5

0.3125

6

0.375

7

0.4375

8

0.5

9

0.5625

10

0.625

11

0.6875

12

0.75

13

0.8125

14

0.875

15

0.9375

 

In.

ft.

1

0.0833

2

0.1667

3

0.2500

4

0.3333

5

0.4167

6

0.5000

7

0.5833

8

0.6667

9

0.7500

10

0.8333

11

0.9167

 

 

Avoirdupois
16 dr. make 1 oz.
16 oz. make 1 lb.
14lb make 1 stone
28lb make 1 qr.
4 qrs. make 1 cwt.
20 cwt. make 1 ton

Apothecaries
20gr. make 1 scru.
3 scr. make 1 dram
3 dr. make 1 ounce
12 oz. make 1 pound

Troy
24 gr. make 1dwt.
20 dwt. make 1 oz.
12 oz. make 1 lb.

Solid (or cubic)
1728 cu.in. in 1 cu. ft.
27 cu. ft. in 1 cu. yd.

Paper
24 sheets make 1 quire
20 quires make 1 ream

 

 Time
60 seconds make 1 minute
60 minutes makes 1 hour
24 houres make 1 day
7 days make 1 week
4 weeks make 1 month
52 weeks make 1 year

 

Long Measure
2 barley corns make 1 inch
12 inches make 1 foot
3 feet make 1 yard
6 feet make 1 fathom
5½ yards make 1 pole
40 poles make 1 furlong
8 furlongs make 1 mile
3 miles make 1 league
69½ miles make 1 degree

Coal Measure
3 bushels make 1 sack
36 bushels make 1 chaldron

Cloth Measure
2¼ inches make 1 nail
4 nails make 1 quarter
3 quarters make 1 Fl. ell
4 quarters make 1 yard
5 quarters make 1 En. el
6 quarters make 1 Er. el

Dry Measure
2 gallons make 1 peck
4 pecks make 1 bushel
4 bushel make 1 sack
8 bushels make 1 quarter
4 quarters make 1 chaldron
10 quarters make 1 last.

Wine Measure
2 pints make 1 quart
4 quarts make 1 gallon
10 gallons make 1anchor
42 gallons make 1 tierce
63 gallons make 1 hogshead
12 hogsheads make 1 pipe
2 pipes make 1 tun

Ale and Beer
2 pints make 1 quart
4 quarts make 1 gallon
9 gallons make 1 firkin
2 firkins make 1 kilder
2 kilderkins make 1 barrel
1½ barrels make 1 hogshead
2 barrels make 1 punch
3 barrels make 1 butt

Land Measure
9 feet make 1 yard
30¼ yards make 1 pole
40 poles make 1 rod
4 rods make 1 acre

 

 Conversions

Linear Conversions

Converting Inches & Centimeters

Units

Approx

Accurate

in ® cm

´ 2.5

´ 2.54

cm ® in

¸ 2.5

¸ 2.54

 

Converting Feet & Meters

Units

Approx

Accurate

fr ® m

´ 2.5

´ 2.54

m ® ft

¸ 2.5

¸ 2.54

 

Converting Yards & Meters

Units

Approx

Accurate

yd ® m

´ 1

´ 1.094

m ® yd

¸ 1

¸ 1.094

 

Converting Miles & Kilometers

Units

Approx

Accurate

mi ® km

´ 1.5

´ 1.609

km ® mi

¸ 1.5

¸ 1.609

 

Use these to convert distance measurements from system to system.

Also, note nautical miles (knots) are different than land measured miles.

Units

Approx

Accurate

knots ® miles

´ 1.2

´ 1.15

miles ® knots

¸ 1.2

¸ 1.15

 

Area Conversions

Converting Inches & Centimeters

Units

Approx

Accurate

in ® cm

´ 6.5

´ 6.452

cm ® in

¸ 6.5

¸ 6.452

 

Converting Feet & Meters

Units

Approx

Accurate

ft ® m

¸ 11

´ 0.764

m ® ft

´ 11

¸ 0093

 

Converting Yards & Meters

Units

Approx

Accurate

yd ® m

´ 1

´ 0.836

m ® yd

¸ 1

´ 1.196

 

Converting Miles & Kilometers

Units

Approx

Accurate

mi ® km

´ 2.5

´ 2.590

km ® mi

¸ 2.5

´ 0.386

 

Use these to convert surface area measurements from system to system.

 

 Volume Conversions

Converting Inches & Centimeters

Units

Approx

Accurate

in ® cm

´ 16

´ 16.387

cm ® in

¸ 16

¸ 0.061

 

Converting Feet & Meters

Units

Approx

Accurate

ft ® m

¸ 35

´ 0.028

m ® ft

´ 35

´ 35.315

 

Converting Yards & Meters

Units

Approx

Accurate

yd ® m

´ 1

´ 0.765

m ® yd

¸ 1

´ 1.308

 

Converting Miles & Kilometers

Units

Approx

Accurate

mi ® km

´ 1.5

´ 1.609

km ® mi

¸ 1.5

¸ 1.609

 

Use these to convert cubic measurements from system to system.

 

Other Conversions

Converting Gallons & Liters

Units

Approx

Accurate

gal ® l

´ 4

´ 3.78

l ® gal

¸ 4

´ 0.264

 

A final note on this topic, a liter is 1000 cubic centimeters in displacement.

 

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