Unit conversion is rewriting a measurement in a different unit without changing the amount, such as writing 3 feet as 36 inches. You multiply by a conversion factor, a fraction equal to 1 such as 12 in1 ft. Converting to a smaller unit gives a larger number; converting to a larger unit gives a smaller number.
In Spanish
conversión de unidades
Also called
converting units, measurement conversion, dimensional analysis, unit analysis
Each conversion factor equals 1, so it changes the unit but not the length. Arrange each factor so the unit you are leaving cancels.
Formal definition and notation
A conversion factor is a ratio of two equal measurements, such as 12 in1 ft, so its value is 1 and multiplying by it changes the unit but not the quantity. Units are treated like factors: a unit in a numerator cancels the same unit in a denominator. This bookkeeping is called dimensional analysis. Several factors can be chained for multi-step conversions, and for area or volume each length factor is applied twice or three times, so 1 ft2 = 144 in2.
Symbol
Read it as
Meaning
12 in1 ft
12 inches per 1 foot
a conversion factor; it equals 1 because 12 in and 1 ft are the same length
ft2
square feet
a unit of area; 1 ft2 = 12 × 12 = 144 in2
≈
is approximately equal to
used for rounded factors between systems, such as 1 mi ≈ 1.61 km
Key facts
US customary length: 12 in = 1 ft, 3 ft = 1 yd, 5,280 ft = 1 mi. Weight: 16 oz = 1 lb, 2,000 lb = 1 ton.
Metric units go up and down by powers of 10: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1,000 g, 1 L = 1,000 mL. See meter and centimeter.
Between systems: 1 in = 2.54 cm, 1 mi ≈ 1.61 km, 1 lb ≈ 0.45 kg, 1 qt ≈ 0.95 L.
Time is not base 10: 60 s = 1 min, 60 min = 1 h, 24 h = 1 day. So 1.5 hours is 1 hour 30 minutes.
For area, square the length factor: 1 yd2 = 9 ft2. For volume, cube it: 1 yd3 = 27 ft3.
Conversion factor method
Conversion factor method
new amount = old amount × new unitold unit
old unit
the unit you start with; put it in the denominator so it cancels
new unit
the unit you want; put it in the numerator
Example: 250 cm × 1 m100 cm = 2.5 m. If the units do not cancel, the factor is upside down.
Try it: metric staircase
Interactive
Type a value and choose the from and to units. Each step down the staircase multiplies by 10, and each step up divides by 10. Try 2.5 kg to grams, then 750 mg to grams.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
A unit rate compares two different quantities per one unit, such as 55 miles per 1 hour. Unit conversion keeps one quantity and changes its unit, such as 1 hour = 60 minutes.
A scale factor changes the actual size of a figure, for example doubling every side. A unit conversion leaves the size the same and only renames it: 1 yard and 3 feet are the same length.
Quick check: 3 questions
Question 1 of 3
How many inches are in 4.5 feet?
Show answer and explanation
Answer: B. Multiply by 12 inches per foot: 4.5 × 12 = 54. 0.375 divides by 12, 16.5 adds 12, and 45 multiplies by 10 as if it were a metric conversion.
Question 2 of 3
Which conversion factor changes 250 centimeters into meters?
Show answer and explanation
Answer: A. Centimeters must be on the bottom to cancel, and 1 m = 100 cm, so 250 × 1100 = 2.5 m. The second choice is upside down, and the other two use the wrong number of centimeters in a meter.
Question 3 of 3
A room is 4 yards long and 5 yards wide. What is its area in square feet?
Show answer and explanation
Answer: D. Convert each side first: 12 ft by 15 ft, so the area is 12 × 15 = 180 square feet. 20 is the area in square yards, 60 multiplies it by 3 instead of 9, and 540 multiplies by 27, the volume factor.
Unit Conversion: frequently asked questions
How do you convert units?
Find a fact that links the two units, such as 1 ft = 12 in, and write it as a fraction with the unit you are leaving on the bottom. Multiply your measurement by that fraction and cancel the matching units. For 30 in: 30 × 1 ft12 in = 2.5 ft. For far-apart units, chain several fractions.
Do you multiply or divide when converting units?
Multiply when you go to a smaller unit, and divide when you go to a larger one. Feet to inches: multiply by 12, since there are more inches. Inches to feet: divide by 12. The conversion factor method handles this for you, because a fraction with the old unit on the bottom does the right operation automatically.
What is dimensional analysis?
Dimensional analysis is the method of carrying units through a calculation and canceling them like factors. It is the same as using conversion factors, written in one chain. Because the units must cancel to leave exactly the unit you want, it also checks your setup: an answer in in2ft shows a factor is upside down.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 4.MD.A.1, CCSS 5.MD.A.1, CCSS 6.RP.A.3.d
Cite this entry
Effortless Math Team. “Unit Conversion.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/unit-conversion/
Flashcard
TermUnit Conversionmultiply by a factor equal to 1
DefinitionChanging a measurement’s unit, not its amount. 5 yd × 3 ft1 yd = 15 ft.
Conversion FactorA conversion factor is a fraction whose top and bottom are the same amount written in different units, such as 12 in1 ft, so it equals 1. Multiplying a measurement by it changes the units without changing the amount: 5 ft × 12 in1 ft = 60 in. Pick the version that cancels the unit you start with.Measurement · Grade 6, Grade 7, Algebra 1RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8NumeratorThe numerator is the top number in a fraction. It tells how many parts are being counted, while the denominator below the fraction bar tells how many equal parts make one whole. In 35, the numerator is 3: three of five equal parts are taken.Number System · Grade 3, Grade 4, Grade 5DenominatorThe denominator is the bottom number in a fraction. It tells how many equal parts make one whole: in 35, the 5 means the whole is cut into 5 equal parts, and the numerator 3 counts the parts you have. The denominator can never be 0.Number System · Grade 3, Grade 4, Grade 5Dimensional AnalysisDimensional analysis is a way to solve problems by tracking the units: you multiply by conversion factors, cancel any unit that appears on both the top and the bottom, and check that the units left over are the ones the answer needs. It is also called the factor-label method or unit analysis.Measurement · Grade 7, Grade 8, Algebra 1VolumeVolume measures the amount of space inside a three-dimensional figure, in cubic units such as cubic centimeters or cubic feet. You can find it by counting the unit cubes that fill the solid. For a rectangular prism, V = l × w × h; for any prism, it equals the area of the base multiplied by the height.Geometry · Grade 5, Grade 6, Grade 7LengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3PowerA power is a number written as a base with an exponent, such as 53, or the value that results, 53 = 5 × 5 × 5 = 125. We say 125 is the third power of 5, or “5 to the third power”. The second power is called the square and the third power the cube.Number System · Grade 5, Grade 6, Grade 7MeterA meter (m) is a metric unit of length equal to 100 centimeters. It is the base unit of length in the metric system, a little over three feet (about 3.28 feet). A doorway is about 2 meters tall, and 1,000 meters make a kilometer. To change meters to centimeters, multiply by 100.Measurement · Grade 3, Grade 4, Grade 5CentimeterA centimeter is a metric unit of length equal to one hundredth of a meter, about the width of a fingernail. Its symbol is cm. There are 100 centimeters in 1 meter and 10 millimeters in 1 centimeter, and 1 inch equals 2.54 centimeters.Measurement · Grade 3, Grade 4, Grade 5SquareA square is a quadrilateral with four equal sides and four right angles. It is a special rectangle and a special rhombus at the same time. For a square with side s, the perimeter is 4s, the area is s2, and each diagonal is s√2.Geometry · Kindergarten, Grade 2, Grade 3InchAn inch is a US customary unit of length equal to one twelfth of a foot, about the width of an adult thumb. Its abbreviation is in. Rulers split each inch into halves, quarters, eighths and sixteenths. One inch is exactly 2.54 centimeters, and 12 inches make 1 foot.Measurement · Grade 2, Grade 3, Grade 4NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2MileA mile (mi) is a US customary unit of length for long distances, equal to 5,280 feet or 1,760 yards. One mile is about 1.61 kilometers, so it is longer than a kilometer. Road distances and speed limits in the United States use miles and miles per hour.Measurement · Grade 4, Grade 5, Grade 6FootA foot is a US customary unit of length equal to 12 inches, about the length of a standard school ruler. Its abbreviation is ft, and its plural is feet. There are 3 feet in a yard and 5,280 feet in a mile, and 1 foot is exactly 30.48 centimeters.Measurement · Grade 2, Grade 3, Grade 4Unit RateA unit rate is a rate that compares a quantity to one unit of another quantity, such as 50 miles per hour or 4 dollars per notebook. To find it, divide the first quantity by the second: 150 miles in 3 hours is 150 ÷ 3 = 50 miles per hour. The word per means for each one.Ratios and Proportions · Grade 6, Grade 7, Grade 8Scale FactorA scale factor is the number used to multiply side lengths when making a similar figure larger or smaller. A scale factor of 2 doubles every length, and a scale factor of 12 makes lengths half as large. Find it by dividing a new length by the matching original length. Areas change by the square of the scale factor.Ratios and Proportions · Grade 7, Grade 8, Algebra 1MultiplicationMultiplication is the operation that combines equal groups to find a total. The fact 4 × 6 = 24 means 4 groups of 6, or 6 + 6 + 6 + 6. The numbers you multiply are called factors, and the result is the product. Order does not matter: 6 × 4 is also 24.Operations · Grade 2, Grade 3, Grade 4DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6ProportionA proportion is an equation that says two ratios are equal, such as 12 = 36. It is read 1 is to 2 as 3 is to 6. In a true proportion the cross products are equal, which lets you find a missing value. Proportions are often used to solve scale, percent, and rate problems.Ratios and Proportions · Grade 6, Grade 7, Grade 8AreaArea is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.Geometry · Grade 3, Grade 4, Grade 5KilometerA kilometer (km) is a metric unit of length equal to 1,000 meters, roughly six tenths of a mile. It measures long distances, such as the length of a road race or the distance between towns. To change kilometers to meters, multiply by 1,000: 3 km is 3,000 m.Measurement · Grade 4, Grade 5, Grade 6Metric SystemThe metric system is a system of measurement in which units are related by powers of 10. Its base units are the meter for length, the gram for mass and the liter for capacity. Prefixes name larger and smaller units: kilo- means 1,000, centi- means one hundredth and milli- means one thousandth, so 1 km = 1,000 m.Measurement · Grade 4, Grade 5, Grade 6