# Converting Between Scale Types of Historic & Modern Maps, page 3

## Converting Lexical Scale to Representative Fraction (RF)/Ratio Scale

### English and Metric **Measures of Length** to use:

**1 inch (in)** = 2.54 centimeters

**1 centimeter (cm)** = 0.39 inch

**1 foot (ft)** = 12 inches = 30.5 centimeters = 0.3 meter

**1 yard (yd)** = 36 inches = 3 feet = 91.44 centimeters = 0.9 meter

**1 meter (m)** = 100 centimeters = 39.37 inches = 3.28 feet = 1.09 yards

**1 mile (mi)** = 63,360 inches = 5,280 feet = 1,760 yards = 1.609 kilometers

**1 nautical mile** = 1,852 meters = 1.852 kilometers

**1 kilometer (km)** = 1,000 m = 100,000 cm = 1,094 yards = 0.6 mile

NOTE: When you carry out any calculation with fractions, make sure that all units in equation are cancelled correctly. If necessary, invert the RF for that purpose.

### 1) IN ENGLISH UNITS

Converting Lexical Scale **"1 inch represents 3.9 miles"** to Representative Fraction (RF) & Ratio:

First, I write the lexical scale as a fraction - 1 inch (on the map) / 3.9 miles (on the ground), then I convert the length unit *mile* to *inches* because the RF shows how many inches on the ground are represented by 1 inch on a map.

I should round the denominator of the resulting fraction so that it does not imply more accuracy than the original precision warranted. So the resulting fraction is 1/250,000 corresponding to a ratio 1:250,000.

Because 1 mile = 5,280 feet x 12 inches = 63,360 inches, I can write the formula for converting Lexical Scale to the RF/Ratio Scale in **English units** this way:

**if Lexical Scale = "1 inch represents A (miles)", then:**

where: **A (miles)** - distance on the ground represented by 1 inch on a map.

### 2) IN METRIC UNITS

Converting Lexical Scale **"6 cm represent 1.5 km"** to RF/Ratio:

As in a previous case, I express the lexical expression as a fraction - "6 cm / 1.5 km" and convert *kilometres* to *centimeters*, so that the numerator has a "1" in a resulting fraction, and both numerator and denominator have the same units:

By solving this equation, I converted a lexical expression "6 cm represent 1.5 km" to a scale as a RF - 1/25,000, or as a Ratio - 1:25,000.

Knowing that 1 km = 100,000 centimetres, I can express the formula for determining the map scale from just a verbal expression in **metric units**:

**if Lexical Scale = "B (cm) represent C (km)", then:**

**and:**

where:

**RF** - Representative Fraction Scale of the map,

**A (cm)** - actual distance - a number of centimetres on the ground, represented by 1 centimetre on a map,

**B (cm)** - distance on a map,

**C (km)** - distance on the ground represented by "B" on a map.

And the formula for converting Lexical Scale **"1 cm represents A km"** to RF & Ratio would look like this:

**if "1 cm represents A (km)", then:**

where **A (km)** - distance on the ground represented by 1 cm on a map.

**< Previous** | Converting Bar Scale to RF/Ratio Scale |

| Converting RF/Ratio Scale to Lexical Scale |

| Converting Lexical Scale to RF/Ratio Scale |

**Back to Basic Calculations for Map Research page**

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