How to convert area measurements between 10 common units.
Goal:
Theory:
Part 1
There are many different units of area, such as ‘square centimeters’, ‘hectares’, ‘square feet’ and ‘acres’.
To change the units of a quantity, it is multiplied or divided by some constant value, called a conversion factor.
This table lists ten different area units, and values that will help you change units of area measurements:
| Unit Name | Unit Symbol | Metric Equivalent | Imperial Equivalent |
| Metric… | |||
|
square centimetre |
cm² | 1 cm² = 100 mm² | 1 cm² = 0.1550 in² |
|
square metre |
m² | 1 m² = 10,000 cm² | 1 m² = 1.1960 yd² |
|
hectare |
ha | 1 ha = 10,000 m² | 1 ha = 2.4711 acres |
|
square kilometre |
km² | 1 km² = 100 ha | 1 km² = 0.3861 mile² |
| Imperial… | Unit Symbol | Imperial Equivalent | Metric Equivalent |
| square inch | in² | 1 in² = 6.4516 cm² | |
| square foot | ft² | 1 ft² = 144 in² | 1 ft² = 0.0929 m² |
| square yard | yd² | 1 yd² = 9 ft² | 1 yd² = 0.8361 m² |
| acre | acre | 1 acre = 4840 yd² | 1 acre = 4046.9 m² |
| square mile | mile² | 1 mile² = 640 acres | 1 mile² = 2.59 km² |
This is how you can change the units of an area measurement:
If possible, find an equation in the table that contains both the units you are converting from and the units you are converting to.
Example 1 – Convert 25 yd² to m²
1 yd² = 0.8361 m²
The number: ‘0.8361’ is the conversion factor.
To convert the units on the left to the units on the right, you multiply by the conversion factor.
To convert the right hand units to the left hand units, you divide by the conversion factor.
So to change 25 yd² to square meters, multiply by 0.8361 …
25 yd² × 0.8361 = 20.9025 m²
Example 2 – Convert 3.5 hectares to km²
1 km² = 100 ha
The number: ‘100’ is the conversion factor.
To convert the units on the left to the units on the right, you multiply by the conversion factor.
To convert the right hand units to the left hand units, you divide by the conversion factor.
So to change 3.5 ha to km², divide by 100 …
3.5 ha ÷ 100 = 0.035 km²
Example 3 – Convert 2.5 square miles to hectares
Step 1: Use this equation to convert square miles to square kilometers:
1 mile² = 2.59 km²
To convert the units on the left to the units on the right, you multiply by the conversion factor.
2.5 mile² × 2.59 = 6.475 km²
Step 2: Use this equation to convert square kilometers to hectares:
1 km² = 100 ha
To convert the units on the left to the units on the right, you multiply by the conversion factor.
6.475 km² × 100 = 647.5 ha
Method:
Part 2
To help you to quickly change units for your own areas, follow the steps below…
Step 1 Download the free support file…
We have created a Maths Helper Plus document to complement this topic. You can use it to practice the steps described below, and as a starting point for solving your own problems.
File name: ‘Area Unit Conversion.mhp’ File size: 37kb
Click here to download the file.If you choose ‘Open this file from its current location’, then Maths Helper Plus should open the document immediately. If not, try the other option: ‘Save this file to disk’, then run Maths Helper Plus and choose the ‘Open’ command from the ‘File’ menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.
Step 2 Convert an area to new units
We will use example 3 (above) to illustrate the procedure. To convert 2.5 square miles to hectares:
Ten different area units are listed. Click beside the units you are converting from:
The pop-up dialog box allows you to enter a value in square miles. Click on the edit box and enter your value:
Click the ‘Run’ button on the dialog box:
The conversion table will display on the text view as shown below. The yellow highlight shows the conversion we were looking for. Some rounding off may be needed.
HINT: If the popup dialog box is in the way, click in the title bar at the top of the dialog box, then drag it to a new location.
Output
Convert 2.5 square miles to:
——————————————————–
METRIC UNITS
1. Square millimetres 2.5 mile² × 2,589,980,000,000 = 6474950000000 mm²
2. Square centimetres 2.5 mile² × 25,899,800,000 = 64749500000.00 cm²
3. Square metres 2.5 mile² × 2,589,980 = 6474950.0000000000 m²
4. Hectares 2.5 mile² × 258.998 = 647.495000000000 ha
5. Square kilometres 2.5 mile² × 2.58998 = 6.474950000000 km²
IMPERIAL UNITS
6. Square inches 2.5 mile² × 4014489600.00 = 10036224000.000 in²
7. Square feet 2.5 mile² × 27878400.00 = 69696000.00000 ft²
8. Square yards 2.5 mile² × 3097600 = 7744000.00000000 yd²
9. Acres 2.5 mile² × 640 = 1600.0000000000 acres
Click the ‘Reset’ button on the dialog box to clear these results from the screen.
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