Feet and Inches Calculator
This feet and inches calculator performs arithmetic on imperial measurements. Add, subtract, multiply, and divide values in feet and inches with automatic simplification, carrying, and borrowing. Convert results to decimal feet, inches, centimeters, and meters.
Feet and Inches Calculator
Add, subtract, multiply, and divide measurements in feet and inches with precision.
Frequently Asked Questions
How do you add feet and inches?
To add feet and inches, add the feet together and the inches together separately. If the total inches equal or exceed 12, divide by 12. The quotient becomes additional feet and the remainder is the remaining inches. For example, 5'8" + 3'7" = 8'15". Since 15 inches = 1 foot 3 inches, the result is 9'3". This carrying process is similar to adding hours and minutes.
How do you subtract feet and inches?
To subtract feet and inches, subtract the inches first, then the feet. If the inches being subtracted are larger, borrow 1 foot (12 inches) from the feet column. For example, 7'3" - 2'8": since 3 is less than 8, borrow 1 foot to get 6'15", then subtract: 6'15" - 2'8" = 4'7". This borrowing process is the same concept as borrowing in standard subtraction.
How do you convert feet and inches to decimal?
To convert feet and inches to decimal feet, divide the inches by 12 and add to the feet. For example, 5'6" = 5 + 6/12 = 5.5 feet. For 8'3" = 8 + 3/12 = 8.25 feet. For inches that don't divide evenly, round as needed: 5'7" = 5 + 7/12 = 5.583 feet. To convert back, take the decimal part and multiply by 12 to get inches: 0.583 × 12 = 7 inches.
How many inches are in a foot?
There are exactly 12 inches in 1 foot. This is a fundamental unit conversion in the imperial system. Other useful conversions include: 1 yard = 3 feet = 36 inches, 1 mile = 5,280 feet = 63,360 inches. In the metric system, 1 foot equals exactly 30.48 centimeters or 0.3048 meters. The 12-inch foot has been standardized internationally since 1959.
How do you convert feet and inches to centimeters?
First convert the measurement entirely to inches: multiply feet by 12 and add the remaining inches. Then multiply the total inches by 2.54 to get centimeters. For example, 5'10" = (5 × 12) + 10 = 70 inches. 70 × 2.54 = 177.8 cm. To convert back from centimeters to feet and inches, divide by 2.54 to get inches, then divide by 12 for feet with the remainder as inches.
How do you multiply feet and inches?
To multiply feet and inches by a whole number, first convert to inches, multiply, then convert back. For example, 3'4" × 3: convert to 40 inches, multiply by 3 = 120 inches, then convert back: 120 ÷ 12 = 10'0". For multiplying two measurements (area), convert both to decimal feet first, multiply, and the result is in square feet. For example, 5'6" × 3'4" = 5.5 × 3.333 = 18.33 sq ft.
How do you read a tape measure?
A standard tape measure marks inches with the longest lines, and subdivides each inch into fractions. The 1/2-inch mark is the next longest, followed by 1/4-inch, 1/8-inch, and 1/16-inch marks (each progressively shorter). Feet are typically marked with a different color or larger number. To read a measurement, count the whole inches from the nearest foot mark, then identify the closest fraction line. For example, a mark 3 small lines past 5 inches on a 1/16" tape reads 5-3/16".
How Feet and Inches Arithmetic Works
Feet and inches use a base-12 system for the inches component. This differs from the decimal system used for metric units, which is why carrying and borrowing must be done at the 12-inch boundary rather than at 10.
Addition rule: Add feet to feet and inches to inches separately. When the inch total reaches 12 or more, subtract 12 inches and carry 1 foot.
Subtraction rule: Subtract feet from feet and inches from inches. When the inch subtrahend is larger, borrow 1 foot (12 inches) from the feet column before subtracting.
Conversion Formulas
| Conversion | Formula |
|---|---|
| Feet + Inches → Total Inches | (feet × 12) + inches |
| Total Inches → Decimal Feet | total inches ÷ 12 |
| Inches → Centimeters | inches × 2.54 |
| Inches → Meters | inches × 0.0254 |
| Meters → Inches | meters ÷ 0.0254 |
| Centimeters → Inches | centimeters ÷ 2.54 |
The conversion factor 1 inch = 2.54 cm is exact by international agreement since 1959.
Step-by-Step Addition Example
Problem: 5′ 9″ + 3′ 7″
- Add inches: 9 + 7 = 16 inches
- 16 ≥ 12, so carry: 16 − 12 = 4 inches remaining, 1 extra foot
- Add feet: 5 + 3 + 1 (carried) = 9 feet
- Result: 9′ 4″
Metric check: 9′ 4″ = 112 inches × 0.0254 = 2.84 m
Step-by-Step Subtraction Example
Problem: 8′ 3″ − 2′ 8″
- Try to subtract inches: 3 − 8 is negative, so borrow
- Borrow 1 foot from the 8: now 7′ 15″ − 2′ 8″
- Subtract inches: 15 − 8 = 7 inches
- Subtract feet: 7 − 2 = 5 feet
- Result: 5′ 7″
Reading a Tape Measure
A standard imperial tape measure divides each inch into progressively shorter tick marks:
- Longest mark — whole inch
- Second longest — ½ inch (0.5″)
- Third — ¼ inch (0.25″)
- Fourth — ⅛ inch (0.125″)
- Shortest — 1/16 inch (0.0625″)
To read a measurement, identify the last whole-inch number, then count the fractional marks past it. For example, a mark two ticks past 5″ on a 1/16″ tape reads 5-2/16″ = 5-1/8″.
Common Length References
| Object | Approximate Length |
|---|---|
| Standard door height | 6′ 8″ (80 inches / 2.03 m) |
| US ceiling height | 8′ 0″ (96 inches / 2.44 m) |
| King bed width | 6′ 4″ (76 inches / 1.93 m) |
| Full sheet of plywood | 4′ × 8′ (1.22 m × 2.44 m) |
| One story of a building | ~10′ (3.05 m) |
Decimal Feet vs. Feet-and-Inches
Surveyors and engineers often use decimal feet (e.g., 5.75 ft) rather than feet-and-inches (5′ 9″) because decimal arithmetic requires no carrying at 12. To convert:
- Feet-and-inches → Decimal feet: divide inches by 12 and add to feet. Example: 5′ 9″ = 5 + 9/12 = 5.75 ft
- Decimal feet → Feet-and-inches: take the decimal part and multiply by 12. Example: 5.75 ft → 0.75 × 12 = 9 inches → 5′ 9″
Fractional Inches in Construction
Lumber dimensions, door frames, and rough framing commonly use fractional inches (⅛, ¼, ⅜, ½, ⅝, ¾, ⅞). When calculating with fractions, convert to decimal inches first:
| Fraction | Decimal |
|---|---|
| 1/16 | 0.0625 |
| 1/8 | 0.125 |
| 3/16 | 0.1875 |
| 1/4 | 0.25 |
| 3/8 | 0.375 |
| 1/2 | 0.5 |
| 5/8 | 0.625 |
| 3/4 | 0.75 |
| 7/8 | 0.875 |
This calculator accepts decimal inches (e.g., enter 0.5 for ½ inch), so you can work with any fraction by converting it first.
Imperial vs. Metric in Practice
The imperial system (feet and inches) is the primary measurement system in the United States for construction, real estate, and everyday use. Most other countries use the metric system (meters, centimeters, millimeters). When working on international projects or purchasing metric materials for imperial drawings, accurate conversion is critical.
Key reference points:
- 1 foot = 30.48 cm (exact)
- 1 meter ≈ 3 ft 3.37 in (3.28084 ft)
- 1 inch = 25.4 mm (exact)
- 1 yard = 3 feet = 0.9144 m