A 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.
The factor 12 in1 ft is a fancy way to write 1. Feet cancel, inches remain, and the length stays the same.
Formal definition and notation
If a units of type A measure the same quantity as b units of type B, then b Ba A and a Ab B are conversion factors; each equals 1. Multiplying a quantity measured in A by b Ba A cancels A and expresses the same quantity in B. Some factors are exact by definition (1 in = 2.54 cm); others are rounded (1 mi is about 1.61 km).
Key facts
A conversion factor equals 1, because its top and bottom are equal amounts. That is why multiplying by it is allowed.
Put the unit you have on the bottom so it cancels, and the unit you want on top.
Converting to a smaller unit makes the number bigger (5 ft is 60 in); converting to a larger unit makes it smaller.
For square units, use the factor twice: 1 yd2 = 3 × 3 = 9 ft2. For cubic units, three times: 1 yd3 = 27 ft3.
You can chain factors: hours to minutes to seconds. Chaining them on purpose is called dimensional analysis.
Using a conversion factor
Using a conversion factor
new amount = old amount × new unitold unit
new unitold unit
the conversion factor, with the unit you want on top and the unit you have on the bottom
Every equivalence gives two factors. From 1 h = 60 min: 60 min1 h turns hours into minutes and 1 h60 min turns minutes into hours.
Try it: metric conversions
Interactive
Type a value and choose two metric units. Each step on the staircase is a factor of 10, so the converter multiplies by the matching conversion factor, such as 1000 mm1 m.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Conversion Factor examples, step by step
Example 1: Hours to minutes
Warm-up
Convert 3.5 hours to minutes.
Equivalence: 1 h = 60 min. Hours must cancel, so hours go on the bottom.
3.5 h × 60 min1 h = 210 min.
Answer: 3.5 hours is 210 minutes.
Example 2: Centimeters to inches
Core
A poster is 250 cm tall. How tall is it in inches? (1 in = 2.54 cm)
You have cm and want in, so use 1 in2.54 cm.
250 cm × 1 in2.54 cm = 2502.54 in.
250 ÷ 2.54 ≈ 98.4.
Answer: The poster is about 98.4 inches tall.
Example 3: Square units
Test-style
A rug covers 3 square yards. How many square feet is that? (1 yd = 3 ft)
A square yard is a square 1 yd by 1 yd, which is 3 ft by 3 ft.
Use the factor twice: 3 yd2 × 3 ft1 yd × 3 ft1 yd.
3 × 9 = 27 ft2. Using the factor once would give the wrong answer 9.
Answer: The rug covers 27 square feet.
Common mistakes
✗ Mistake48 in × 12 in1 ft = 576 ft.
✓ Instead48 in × 1 ft12 in = 4 ft.
With the factor upside down, inches do not cancel (you get square inches per foot). Write the units and check that the starting unit cancels.
✗ Mistake2 yd2 = 2 × 3 = 6 ft2.
✓ Instead2 yd2 = 2 × 3 × 3 = 18 ft2.
Area has two dimensions, so the length factor is applied twice. Volume needs it three times.
✗ Mistake2.5 hours is 250 minutes.
✓ Instead2.5 × 60 = 150 minutes.
Time units are not base 10. An hour has 60 minutes, so the conversion factor is 60 min1 h, not 100.
A scale factor changes the size of a figure (a 2 cm drawing of a 6 cm object uses factor 3). A conversion factor never changes size; it only renames the units.
A unit rate compares two different quantities, like 60 miles per 1 hour. A conversion factor compares the same quantity in two units, like 12 inches per 1 foot, so it always equals 1.
Quick check: 3 questions
Question 1 of 3
Which conversion factor changes 90 minutes into hours?
Show answer and explanation
Answer: B. Minutes must cancel, so minutes go on the bottom: 90 × 160 = 1.5 h. A has minutes on top and would give 5400; C and D use 100 minutes per hour, which is false.
Question 2 of 3
How many inches are in 7 feet?
Show answer and explanation
Answer: A.7 ft × 12 in1 ft = 84 in. 19 adds 12, 0.58 divides by 12 (factor upside down), and 70 treats a foot as 10 inches.
Question 3 of 3
A tank holds 2 cubic yards of sand. How many cubic feet is that?
Show answer and explanation
Answer: C.1 yd3 = 3 × 3 × 3 = 27 ft3, so 2 cubic yards is 54 cubic feet. 6 uses the factor once, 18 twice, and 27 forgets the 2.
Conversion Factor: frequently asked questions
Why does a conversion factor equal 1?
Its numerator and denominator name the same amount. 12 inches and 1 foot are the same length, so 12 in1 ft is like 55: a quantity divided by itself. Multiplying any measurement by 1 leaves its size unchanged, and only the units change.
How do I know which way to flip a conversion factor?
Write the units in. Put the unit you are starting with in the denominator so it cancels, and the unit you want in the numerator. Converting 300 cm to meters uses 1 m100 cm, so cm cancels and you get 3 m. If the units do not cancel, flip the factor.
What is the conversion factor from inches to centimeters?
One inch is exactly 2.54 centimeters, so the factors are 2.54 cm1 in (inches to centimeters) and 1 in2.54 cm (centimeters to inches). This value is exact by definition, so answers that use it are only as rounded as your final step.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.RP.A.3.d
Cite this entry
Effortless Math Team. “Conversion Factor.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/conversion-factor/
Flashcard
TermConversion Factor12 in1 ft
DefinitionA fraction equal to 1 that renames units. 5 ft × 12 in1 ft = 60 in: feet cancel, inches remain.
NumberA 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 2SquareA 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 3Dimensional 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 1InchAn 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 4YardA yard (yd) is a US customary unit of length equal to 3 feet or 36 inches. It is a little shorter than a meter: 1 yard is exactly 0.9144 meter. Yards measure fabric, rooms, gardens and the length of a football field, which is 100 yards between the goal lines.Measurement · Grade 2, Grade 3, Grade 4FootA 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 4LengthLength 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 3VolumeVolume 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 7Scale 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 1Unit 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 8MileA 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 6NumeratorThe 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 5MeterA 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 5Unit ConversionUnit 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.Measurement · Grade 4, Grade 5, Grade 6RatioA 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 8Metric 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 6DensityDensity is the amount of mass packed into each unit of volume, found by dividing mass by volume: D = mV. Its units combine the two, such as grams per cubic centimeter. A 40 g block with a volume of 16 cm³ has D = 40 ÷ 16 = 2.5 g/cm³. Population density works the same way: people per unit of area.Problem Solving · Grade 8, Algebra 1, GeometryKilometerA 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 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 8