Difference between revisions of "Measurement (AREA) – CONVERSION"

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(Created page with "===Area=== {| class="wikitable" |+ Area !Name of unit !Symbol !Definition !Relation to SI units |- | acre (international) || ac | ≡ {{nowrap|1 ch × 10...")
 
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
===Area===
+
==Techniques==
 +
 
 +
=== Process overview ===
 +
 
 +
The process of conversion depends on the specific situation and the intended purpose. This may be governed by regulation, contract, technical specifications or other published standards. Engineering judgment may include such factors as:
 +
* The precision and accuracy of measurement and the associated uncertainty of measurement.
 +
* The statistical confidence interval or tolerance interval of the initial measurement.
 +
* The number of significant figures of the measurement.
 +
* The intended use of the measurement including the engineering tolerances.
 +
* Historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot.
 +
 
 +
Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement. This is sometimes called ''soft conversion''. It does not involve changing the physical configuration of the item being measured.
 +
 
 +
By contrast, a ''hard conversion'' or an ''adaptive conversion'' may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system. It sometimes involves a slightly different configuration, or size substitution, of the item. Nominal values are sometimes allowed and used.
 +
 
 +
=== Conversion factors ===
 +
A conversion factor is used to change the units of a measured quantity without changing its value. The '''unity bracket method''' of unit conversion consists of a fraction in which the denominator is equal to the numerator, but they are in different units. Because of the identity property of multiplication, the value of a quantity will not change as long as it is multiplied by one. Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.
 +
 
 +
The following example demonstrates how the unity bracket method is used to convert the rate 5 kilometers per second to meters per second. The symbols km, m, and s represent kilometer, meter, and second, respectively.
 +
 
 +
<math>\frac{5 \cancel {\text {km}}}{\text {s}}
 +
\cdot</math><math>\frac{{1000 }\text { m}}{{1}{\cancel {\text { km}}}}</math><math>=</math><math>\frac{{5000 \cdot {\text {m}}}}{{\text {s}\cdot {1}}}
 +
=</math><math>\frac {5000{\text { m}}}{\text {s}}</math>
 +
 
 +
Thus, it is found that 5 kilometers per second is equal to 5000 meters per second.
 +
 
 +
=== Software tools ===
 +
There are many conversion tools. They are found in the function libraries of applications such as spreadsheets databases, in calculators, and in macro packages and plugins for many other applications such as the mathematical, scientific and technical applications.
 +
 
 +
There are many standalone applications that offer the thousands of the various units with conversions. For example, the free software movement offers a command line utility [https://www.gnu.org/software/units/ GNU units] for Linux and Windows.
 +
 
 +
== Tables of conversion factors ==
 +
 
 
{| class="wikitable"
 
{| class="wikitable"
−
|+ [[Surface area|Area]]
+
|+ Area
 
!Name of unit
 
!Name of unit
 
!Symbol
 
!Symbol
Line 7: Line 39:
 
!Relation to SI units
 
!Relation to SI units
 
|-
 
|-
−
| [[acre]] (international) || ac
+
| acre (international) || ac
−
| ≡ {{nowrap|1 ch × 10 ch}} = {{val|4840|u=sqyd}}
+
| ≡ 1 ch × 10 ch = 4840 sq yd
−
| ≡ {{val|4046.8564224|u=m2}}
+
| ≡ 4 046.856 4224 m<sup>2</sup>
 
|-
 
|-
−
| [[acre]] (US survey) || ac
+
| acre (US survey) || ac
−
| ≡ 10 sq ch = {{val|4840|u=sqyd}}, also {{val|43560|u=sqft}}
+
| ≡ 10 sq ch = 4840 sq yd, also 43 560 sq ft
−
| ≈ {{val|4046.873|u=m2}}
+
| ≈ 4 046.873 m<sup>2</sup>
 
|-
 
|-
−
| [[Hectare#Are|are]] || a
+
| are || a
 
| ≡ 100&nbsp;m<sup>2</sup>
 
| ≡ 100&nbsp;m<sup>2</sup>
 
| ≡ 100&nbsp;m<sup>2</sup>
 
| ≡ 100&nbsp;m<sup>2</sup>
 
|-
 
|-
−
| [[barn (unit)|barn]] || b
+
| barn || b
 
| ≡ 10<sup>−28</sup>&nbsp;m<sup>2</sup>
 
| ≡ 10<sup>−28</sup>&nbsp;m<sup>2</sup>
 
| ≡ 10<sup>−28</sup>&nbsp;m<sup>2</sup>
 
| ≡ 10<sup>−28</sup>&nbsp;m<sup>2</sup>
 
|-
 
|-
 
| barony || &nbsp;
 
| barony || &nbsp;
−
| ≡ {{val|4000}}&nbsp;ac
+
| ≡ 4000 ac
−
| ≡ {{val|1.61874256896|e=7|u=m2}}
+
| ≡ 1.618 742 568 96 x 10<sup>7</sup> m<sup>2</sup>
 
|-
 
|-
 
| board || bd
 
| board || bd
−
| ≡ {{nowrap|1 in × 1 ft}}
+
| ≡ 1 in × 1 ft
−
| ≡ {{val|7.74192|e=-3|u=m2}}
+
| ≡ 7.741 92 x 10<sup>-3</sup> m<sup>2</sup>
 
|-
 
|-
 
| boiler horsepower equivalent direct radiation || bhp EDR
 
| boiler horsepower equivalent direct radiation || bhp EDR
 
| ≡ 1&nbsp;ft<sup>2</sup> × 1&nbsp;bhp / (240&nbsp;BTU<sub>IT</sub>/h)
 
| ≡ 1&nbsp;ft<sup>2</sup> × 1&nbsp;bhp / (240&nbsp;BTU<sub>IT</sub>/h)
−
| ≈ {{val|12.958174|u=m2}}
+
| ≈ 12.958 174 m<sup>2</sup>
 
|-
 
|-
−
| circular [[inch]] || circ in
+
| circular inch || circ in
−
| ≡ {{frac|π|4}}&nbsp;sq&nbsp;in
+
| ≡ <math> \tfrac{\pi}{4}</math> sq in
−
| ≈ {{val|5.067075|e=-4|u=m2}}
+
| ≈ 5.067 075 x 10<sup>-4</sup> m<sup>2</sup>
 
|-
 
|-
 
| circular mil; circular thou || circ mil
 
| circular mil; circular thou || circ mil
−
| ≡ {{frac|π|4}}&nbsp;mil<sup>2</sup>
+
| ≡ <math> \tfrac{\pi}{4}</math> &nbsp;mil<sup>2</sup>
−
| ≈ {{val|5.067075|e=-10|u=m2}}
+
| ≈ 5.067 075 x 10<sup>-10</sup> m<sup>2</sup>
 
|-
 
|-
 
| cord || &nbsp;
 
| cord || &nbsp;
 
| ≡ 192&nbsp;bd
 
| ≡ 192&nbsp;bd
−
| ≡ {{val|1.48644864|u=m2}}
+
| ≡ 1.486 448 64 m<sup>2</sup>
 
|-
 
|-
−
| [[cuerda]] (PR Survey) || cda
+
| cuerda (PR Survey) || cda
−
| ≡ 1 cda x 1 cda = {{val|0.971222}} acre
+
| ≡ 1 cda x 1 cda = 0.971 222 acre
−
| ≡ {{val|3930.395625|u=m2}}
+
| ≡ 3 930.395 625 m<sup>2</sup>
 
|-
 
|-
−
| [[dunam]] || &nbsp;
+
| dunam || &nbsp;
−
| ≡ {{val|1000|u=m2}}
+
| ≡ 1000 m<sup>2</sup>
−
| ≡ {{val|1000|u=m2}}
+
| ≡ 1000 m<sup>2</sup>
 
|-
 
|-
−
| [[guntha]] (India) || &nbsp;
+
| guntha (India) || &nbsp;
 
| ≡ 121&nbsp;sq&nbsp;yd
 
| ≡ 121&nbsp;sq&nbsp;yd
 
| ≈ 101.17&nbsp;m<sup>2</sup>
 
| ≈ 101.17&nbsp;m<sup>2</sup>
 
|-
 
|-
−
| [[hectare]] || ha
+
| hectare || ha
−
| ≡ {{val|10000|u=m2}}
+
| ≡ 10 000 m<sup>2</sup>
−
| ≡ {{val|10000|u=m2}}
+
| ≡ 10 000 m<sup>2</sup>
 
|-
 
|-
−
| [[hide (unit)|hide]] || &nbsp;
+
| hide || &nbsp;
 
| ≈ 120 ac (variable)
 
| ≈ 120 ac (variable)
−
| ≈ {{val|5|e=5|u=m2}}
+
| ≈ 5 x 10<sup>5</sup> m<sup>2</sup>
 
|-
 
|-
 
| rood || ro
 
| rood || ro
−
| ≡ {{frac|4}}&nbsp;ac
+
| ≡ <math> \tfrac{1}{4}</math>&nbsp;ac
−
| = {{val|1011.7141056|u=m2}}
+
| = 1 011.714 1056 m<sup>2</sup>
 
|-
 
|-
 
| ping ||
 
| ping ||
−
| ≡ {{frac|20|11}}&nbsp;m × {{frac|20|11}}&nbsp;m
+
| ≡ <math> \tfrac{20}{11}</math>&nbsp;m × <math> \tfrac{20}{11}</math>&nbsp;m
−
| ≈ {{val|3.306|u=m2}}
+
| ≈ 3.306 m<sup>2</sup>
 
|-
 
|-
 
| section ||
 
| section ||
 
| ≡ 1 mi × 1 mi
 
| ≡ 1 mi × 1 mi
−
| = {{val|2.589988110336|e=6|u=m2}}
+
| = 2.589 988 110 336 x 10<sup>6</sup> m<sup>2</sup>
 
|-
 
|-
−
| [[shed (physics)|shed]] || &nbsp;
+
| shed || &nbsp;
 
| ≡ 10<sup>−52</sup>&nbsp;m<sup>2</sup>
 
| ≡ 10<sup>−52</sup>&nbsp;m<sup>2</sup>
 
| = 10<sup>−52</sup>&nbsp;m<sup>2</sup>
 
| = 10<sup>−52</sup>&nbsp;m<sup>2</sup>
Line 85: Line 117:
 
| square (roofing) ||
 
| square (roofing) ||
 
| ≡ 10 ft × 10 ft
 
| ≡ 10 ft × 10 ft
−
| = {{val|9.290304|u=m2}}
+
| = 9.290 304 m<sup>2</sup>
 
|-
 
|-
 
| square chain (international) || sq ch
 
| square chain (international) || sq ch
−
| ≡ 66 ft × 66 ft = {{frac|10}} ac
+
| ≡ 66 ft × 66 ft = <math> \tfrac{1}{10}</math> ac
−
| ≡ {{val|404.68564224|u=m2}}
+
| ≡ 404.685 642 24 m<sup>2</sup>
 
|-
 
|-
 
| square chain (US Survey) || sq ch
 
| square chain (US Survey) || sq ch
−
| ≡ 66 ft (US) × 66 ft (US) = {{frac|10}} US survey acre
+
| ≡ 66 ft (US) × 66 ft (US) = <math> \tfrac{1}{10}</math> US survey acre
−
| ≈ {{val|404.6873|u=m2}}
+
| ≈ 404.6873 m<sup>2</sup>
 
|-
 
|-
−
| [[square foot]] || sq ft
+
| square foot || sq ft
−
| ≡ {{nowrap|1 ft × 1 ft}}
+
| ≡ 1 ft × 1 ft
−
| ≡ {{val|9.290304|e=-2|u=m2}}
+
| ≡ 9.290 304 x 10<sup>-2</sup> m<sup>2</sup>
 
|-
 
|-
−
| square [[foot (unit)|foot]] (US Survey) || sq ft
+
| square foot (US Survey) || sq ft
−
| ≡ {{nowrap|1 ft (US) × 1 ft (US)}}
+
| ≡ 1 ft (US) × 1 ft (US)
−
| ≈ {{val|9.2903411613275|e=-2|u=m2}}
+
| ≈ 9.290 341 161 3275 x 10<sup>-2</sup> m<sup>2</sup>
 
|-
 
|-
−
| [[square inch]] || sq in
+
| square inch || sq in
−
| ≡ {{nowrap|1 in × 1 in}}
+
| ≡ 1 in × 1 in
−
| ≡ {{val|6.4516|e=-4|u=m2}}
+
| ≡ 6.4516 x 10<sup>-4</sup> m<sup>2</sup>
 
|-
 
|-
−
| [[square kilometre]] || km<sup>2</sup>
+
| square kilometre || km<sup>2</sup>
 
| ≡ 1&nbsp;km × 1&nbsp;km
 
| ≡ 1&nbsp;km × 1&nbsp;km
 
| = 10<sup>6</sup> m<sup>2</sup>
 
| = 10<sup>6</sup> m<sup>2</sup>
Line 113: Line 145:
 
| square link (Gunter's)(International) || sq lnk
 
| square link (Gunter's)(International) || sq lnk
 
| ≡ 1 lnk × 1 lnk ≡ 0.66&nbsp;ft × 0.66&nbsp;ft
 
| ≡ 1 lnk × 1 lnk ≡ 0.66&nbsp;ft × 0.66&nbsp;ft
−
| = {{val|4.0468564224|e=-2|u=m2}}
+
| = 4.046 856 4224 x 10<sup>-2</sup> m<sup>2</sup>
 
|-
 
|-
 
| square link (Gunter's)(US Survey) || sq lnk
 
| square link (Gunter's)(US Survey) || sq lnk
−
| ≡ {{nowrap|1 lnk × 1 lnk}} ≡ {{nowrap|0.66 ft (US) × 0.66 ft (US)}}
+
| ≡ 1 lnk × 1 lnk ≡ 0.66 ft (US) × 0.66 ft (US)
−
| ≈ {{val|4.046872|e=-2|u=m2}}
+
| ≈ 4.046 872 x 10<sup>-2</sup> m<sup>2</sup>
 
|-
 
|-
 
| square link (Ramsden's) || sq lnk
 
| square link (Ramsden's) || sq lnk
 
| ≡ 1 lnk × 1 lnk ≡ 1&nbsp;ft × 1&nbsp;ft
 
| ≡ 1 lnk × 1 lnk ≡ 1&nbsp;ft × 1&nbsp;ft
−
| = {{val|0.09290304|u=m2}}
+
| = 0.092 903 04 m<sup>2</sup>
 
|- style="background:#dfd;"
 
|- style="background:#dfd;"
−
| [[square metre]] (SI&nbsp;unit) || m<sup>2</sup>
+
| square metre (SI&nbsp;unit) || m<sup>2</sup>
−
| ≡ 1 [[Metre|m]] × 1 m
+
| ≡ 1 m × 1 m
 
| = 1 m<sup>2</sup>
 
| = 1 m<sup>2</sup>
 
|-
 
|-
 
| square mil; square thou || sq mil
 
| square mil; square thou || sq mil
 
| ≡ 1 mil × 1 mil
 
| ≡ 1 mil × 1 mil
−
| = {{val|6.4516|e=-10|u=m2}}
+
| = 6.4516 x 10<sup>-10</sup> m<sup>2</sup>
 
|-
 
|-
−
| square [[mile]] || sq mi
+
| square mile || sq mi
 
| ≡ 1&nbsp;mi × 1&nbsp;mi
 
| ≡ 1&nbsp;mi × 1&nbsp;mi
−
| ≡ {{val|2.589988110336|e=6|u=m2}}
+
| ≡ 2.589 988 110 336 x 10<sup>6</sup> m<sup>2</sup>
 
|-
 
|-
−
| square [[mile]] (US Survey) || sq mi
+
| square mile (US Survey) || sq mi
 
| ≡ 1&nbsp;mi (US) × 1&nbsp;mi (US)
 
| ≡ 1&nbsp;mi (US) × 1&nbsp;mi (US)
−
| ≈ {{val|2.58999847|e=6|u=m2}}
+
| ≈ 2.589 998 47 x 10<sup>6</sup> m<sup>2</sup>
 
|-
 
|-
 
| square rod/pole/perch || sq rd
 
| square rod/pole/perch || sq rd
 
| ≡ 1 rd × 1 rd
 
| ≡ 1 rd × 1 rd
−
| = {{val|25.29285264|u=m2}}
+
| = 25.292 852 64 m<sup>2</sup>
 
|-
 
|-
−
| [[square yard]] (International) || sq yd
+
| square yard (International) || sq yd
 
| ≡ 1 yd × 1 yd
 
| ≡ 1 yd × 1 yd
−
| ≡ {{val|0.83612736|u=m2}}
+
| ≡ 0.836 127 36 m<sup>2</sup>
 
|-
 
|-
−
| [[stremma]] || &nbsp;
+
| stremma || &nbsp;
−
| ≡ {{val|1000|u=m2}}
+
| ≡ 1000 m<sup>2</sup>
−
| = {{val|1000|u=m2}}
+
| = 1000 m<sup>2</sup>
 
|-
 
|-
−
| [[survey township|township]] || &nbsp;
+
| township || &nbsp;
 
| ≡ 36 sq mi (US)
 
| ≡ 36 sq mi (US)
−
| ≈ {{val|9.323994|e=7|u=m2}}
+
| ≈ 9.323 994 x 10<sup>7</sup> m<sup>2</sup>
 
|-
 
|-
−
| [[virgate|yardland]] || &nbsp;
+
| yardland || &nbsp;
 
| ≈ 30 ac
 
| ≈ 30 ac
−
| ≈ {{val|1.2|e=5|u=m2}}
+
| ≈ 1.2 x 10<sup>5</sup> m<sup>2</sup>
 
|}
 
|}
  

Latest revision as of 11:59, 17 December 2021

Techniques

Process overview

The process of conversion depends on the specific situation and the intended purpose. This may be governed by regulation, contract, technical specifications or other published standards. Engineering judgment may include such factors as:

  • The precision and accuracy of measurement and the associated uncertainty of measurement.
  • The statistical confidence interval or tolerance interval of the initial measurement.
  • The number of significant figures of the measurement.
  • The intended use of the measurement including the engineering tolerances.
  • Historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot.

Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement. This is sometimes called soft conversion. It does not involve changing the physical configuration of the item being measured.

By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system. It sometimes involves a slightly different configuration, or size substitution, of the item. Nominal values are sometimes allowed and used.

Conversion factors

A conversion factor is used to change the units of a measured quantity without changing its value. The unity bracket method of unit conversion consists of a fraction in which the denominator is equal to the numerator, but they are in different units. Because of the identity property of multiplication, the value of a quantity will not change as long as it is multiplied by one. Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one. So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.

The following example demonstrates how the unity bracket method is used to convert the rate 5 kilometers per second to meters per second. The symbols km, m, and s represent kilometer, meter, and second, respectively.

Thus, it is found that 5 kilometers per second is equal to 5000 meters per second.

Software tools

There are many conversion tools. They are found in the function libraries of applications such as spreadsheets databases, in calculators, and in macro packages and plugins for many other applications such as the mathematical, scientific and technical applications.

There are many standalone applications that offer the thousands of the various units with conversions. For example, the free software movement offers a command line utility GNU units for Linux and Windows.

Tables of conversion factors

Area
Name of unit Symbol Definition Relation to SI units
acre (international) ac ≡ 1 ch × 10 ch = 4840 sq yd ≡ 4 046.856 4224 m2
acre (US survey) ac ≡ 10 sq ch = 4840 sq yd, also 43 560 sq ft ≈ 4 046.873 m2
are a ≡ 100 m2 ≡ 100 m2
barn b ≡ 10−28 m2 ≡ 10−28 m2
barony   ≡ 4000 ac ≡ 1.618 742 568 96 x 107 m2
board bd ≡ 1 in × 1 ft ≡ 7.741 92 x 10-3 m2
boiler horsepower equivalent direct radiation bhp EDR ≡ 1 ft2 × 1 bhp / (240 BTUIT/h) ≈ 12.958 174 m2
circular inch circ in ≡ sq in ≈ 5.067 075 x 10-4 m2
circular mil; circular thou circ mil ≡  mil2 ≈ 5.067 075 x 10-10 m2
cord   ≡ 192 bd ≡ 1.486 448 64 m2
cuerda (PR Survey) cda ≡ 1 cda x 1 cda = 0.971 222 acre ≡ 3 930.395 625 m2
dunam   ≡ 1000 m2 ≡ 1000 m2
guntha (India)   ≡ 121 sq yd ≈ 101.17 m2
hectare ha ≡ 10 000 m2 ≡ 10 000 m2
hide   ≈ 120 ac (variable) ≈ 5 x 105 m2
rood ro ≡  ac = 1 011.714 1056 m2
ping ≡  m ×  m ≈ 3.306 m2
section ≡ 1 mi × 1 mi = 2.589 988 110 336 x 106 m2
shed   ≡ 10−52 m2 = 10−52 m2
square (roofing) ≡ 10 ft × 10 ft = 9.290 304 m2
square chain (international) sq ch ≡ 66 ft × 66 ft = ac ≡ 404.685 642 24 m2
square chain (US Survey) sq ch ≡ 66 ft (US) × 66 ft (US) = US survey acre ≈ 404.6873 m2
square foot sq ft ≡ 1 ft × 1 ft ≡ 9.290 304 x 10-2 m2
square foot (US Survey) sq ft ≡ 1 ft (US) × 1 ft (US) ≈ 9.290 341 161 3275 x 10-2 m2
square inch sq in ≡ 1 in × 1 in ≡ 6.4516 x 10-4 m2
square kilometre km2 ≡ 1 km × 1 km = 106 m2
square link (Gunter's)(International) sq lnk ≡ 1 lnk × 1 lnk ≡ 0.66 ft × 0.66 ft = 4.046 856 4224 x 10-2 m2
square link (Gunter's)(US Survey) sq lnk ≡ 1 lnk × 1 lnk ≡ 0.66 ft (US) × 0.66 ft (US) ≈ 4.046 872 x 10-2 m2
square link (Ramsden's) sq lnk ≡ 1 lnk × 1 lnk ≡ 1 ft × 1 ft = 0.092 903 04 m2
square metre (SI unit) m2 ≡ 1 m × 1 m = 1 m2
square mil; square thou sq mil ≡ 1 mil × 1 mil = 6.4516 x 10-10 m2
square mile sq mi ≡ 1 mi × 1 mi ≡ 2.589 988 110 336 x 106 m2
square mile (US Survey) sq mi ≡ 1 mi (US) × 1 mi (US) ≈ 2.589 998 47 x 106 m2
square rod/pole/perch sq rd ≡ 1 rd × 1 rd = 25.292 852 64 m2
square yard (International) sq yd ≡ 1 yd × 1 yd ≡ 0.836 127 36 m2
stremma   ≡ 1000 m2 = 1000 m2
township   ≡ 36 sq mi (US) ≈ 9.323 994 x 107 m2
yardland   ≈ 30 ac ≈ 1.2 x 105 m2

Licensing

Content obtained and/or adapted from:

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