Length Conversion – Metric and Customary System, Examples

What Is Length Conversion?

Length conversion refers to converting measurements of length or distance from one unit to another. This is typically done to express measurements in a more convenient or appropriate unit for a particular purpose or to compare lengths expressed with 2 different units. 

Example: Suppose you have two ropes, one 15 inches long and the other 2 feet long. Which rope is longer? Can you compare 15 inches with 2 feet? No! 

To compare the lengths, the two measurements must be in the same units. You must convert inches into feet or feet to inches and then compare. This is what we call a length conversion.

1 foot = 12 inches

2 feet = 24 inches > 15 inches

Thus, 2 feet > 15 inches

Length is a fundamental physical quantity, measured in units like meters, centimeters, inches, or feet, used to describe the size of an object from one end to another.

Length Conversion: Definition

Length conversion is the process of converting the length measurements from one unit to another using the correct conversion factor, simplifying the comparison lengths expressed in different units.

Length Conversion in the Metric System

Converting lengths within the metric system is straightforward as it is based on the decimal system and only involves moving a decimal point. In this system, the unit “meter” acts as the base unit of length, and we can obtain smaller or larger units by attaching various prefixes such as kilo, hecto, deka, deci, centi, and milli to it.

Let’s quickly revise these units, their abbreviations, prefixes, and corresponding powers of 10.

Kilometer	Hectometer	Decameter	Meter	Decimeter	Centimeter	Millimeter
km	hm	dam	m	dm	cm	mm
103	102	101	100 = 1	10-1	10-2	10-3

How to Convert Lengths in the Metric System

Length measurement conversion in the metric system can be simplified using the following tricks:

Alt tag: Length conversion in the metric system

• If you move n positions to the right from any place, you move n decimal places to the right. So multiply by 10ⁿ.

Examples:

1. To convert meters (m) into decimeters (dm), multiply by 10. (1 m = 10 dm)
2. To convert kilometers (km) into meters (m), multiply by 1000. (5 km = 5000 m)

• If you move n positions to the left from any place, you move n decimal places to the left. So divide by 10ⁿ (or multiply by 10^-n).

Examples:

1. To convert meters (m) into kilometers (km), divide by 1000. (6 m = 0.006 km)
2. To convert millimeters (mm) into centimeters (cm), divide by 10. (7 mm = 0.7 cm)

Length Conversion in the Customary System

The customary system, primarily used in the United States, employs inches, yards, miles, and feet to measure lengths or distances. This system is based on the English system of measurement (the same system from which the Imperial system is also derived.) 

While the metric system has largely replaced the Imperial system in many countries, the customary system remains prevalent in the United States.

Length conversions in the customary system:

• 1 foot = 12 inches
• 1 yard = 3 feet = 36 inches 
• 1 mile = 5,280 feet 
• 1 mile = 1,760 yards

Length Conversion Chart for the Customary System and Metric System

Here’s a length or distance conversion table for different units of length in the metric system and the customary system.

1 centimeter = 10 millimeters	1 cm = 10 mm
1 decimeter = 10 centimeters	1 dm = 10 cm
1 meter = 100 centimeters	1 m = 100 cm
1 kilometer = 1000 meters	1 km = 1000 m
1 inch = 2.54 centimeters	1 in = 2.54 cm
1 foot = 12 inches	1 ft = 12 in
1 yard = 3 feet = 36 inches	1 yd = 3 ft = 36 in
1 mile = 1,760 yards = 5,280 feet	1 mi = 1,760 yd = 5,280 ft
1 mile ≈ 1.61 kilometers	1 mi ≈ 1.61 km

Length Conversion in the Imperial System

The Imperial system is based on the English units. It’s closely related to the customary system, but the two systems have many differences. 

• Familiar units include the inch, foot, yard, and mile.
• Units for land measurement consist of the furlong, chain, link, rod, pole, perch, and Ramsden’s chain.
• Nautical units include the fathom, shackle, cable, and nautical mile.
• Body measurements encompass the foot, hand, palm, nail, and finger.

Here are different Imperial units for length and their relationships:

1 nail	= $2\frac{1}{4}$inches
4 inches	= 1 hand
12 inches	= 1 foot
3 foot	= 1 yard
5.5 yards	= 1 rod
6 foot	= 1 fathom
22 yards	= 1 chain
100 links	= 1 chain
10 chains	= 1 furlong
8 furlongs	= 1 statute mile
6080 foot	= 1 nautical mile

Length Conversion Table for the Imperial System and Metric System

Imperial Units		Metric Units
1 nautical mile	1.151 miles	1852 meters
1 mile	1760 yards	1609 meters
1 furlong	220 yards	201 meters
1 rod	5.50 yards	5.029 meters
1 fathom	6 feet	1.829 meters
1 yard	3 feet	0.9144 meters
1 foot	12 inches	0.3048 meters
1 Inch	0.083 foot	0.0254 meters

Facts about Length Conversion

Conclusion

​​In this article, we learned about the fundamentals of length conversion in the metric, imperial, and customary systems. Let’s solidify our understanding by solving examples and practicing MCQs for better comprehension.

Solved Examples on Length Conversion

1. Convert 200 m to km.

Solution: 

By the length conversion formula for meters to kilometers, we have

1 km = 1000 m

1 m = $\frac{1}{1000}$ km

200 m = $\frac{200}{1000}$ = 0.2 km

2. Which is longer? 48 inches or 4 feet?

Solution: 

To compare lengths, bring both measurements in the same unit.

1 feet = 12 inches

4 feet = $12 \times 4$ inches = 48 inches

Thus, 48 inches = 4 feet

3. How many inches are there in 6 feet?

Solution: 

1 feet = 12 inches

6 feet = $6 \times 12$ = 72 inches

4. How many millimeters are there in 4 hectometers?

Solution: 

1 hectometer = 100 meter

1 meter = 1000 millimeters

To convert 1 hectometer into millimeters, you move 5 positions to the right.

So multiply by 10⁵ = 1,00,000.

1 hectometer = 1,00,000 millimeters

4 hectometers = 4 × 1,00,000 = 4,00,000 millimeters

5. Which pencil is longer?

Alt tag: 2 pencils, one 6.5 in long and the other 17 cm long

Solution: 

Length of the yellow pencil = 6.5 in

Length of the black pencil = 17 cm

To compare lengths, they must be in the same units.

Let’s convert 6.5 inches into centimeters.

1 inch = 2.54 cm

Length of the yellow pencil = 6.5 inches = 6.5 × 2.54 cm = 16.51 cm

Here, 16.51 cm < 17 cm

Thus, the black pencil is longer.

Practice Problems on Length Conversion