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How to convert convert area measurements between 10 common units.

 This topic is part of the TCS FREE high school mathematics 'How-to Library', and will help you to convert area measurements between 10 common units. (See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

### Theory:

There are many different units of area, such as 'square centimetres', '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 metres, multiply by 0.8361 ...

25 yd² × 0.8361 = 20.9025

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 kilometres:

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 kilometres 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:

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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