How to Add and Subtract Feet and Inches by Hand

Step-by-step method for adding, subtracting, multiplying and dividing feet and inches by hand, with fractional inches and carrying or borrowing 12 inches.

Adding Feet and Inches Is Not Like Adding Decimals

Adding 5' 10" and 3' 8" by learning how to add feet and inches separately works until the inches hit 12 or more. Then it fails. 18 inches is not 18 inches, it is 1 foot 6 inches. The system is base-12 for the foot-inch relationship and base-2 for fractional inches, not base-10. Carry every 12 inches into the feet column. Handle fractions with a common denominator before anything else.

This is not decimal math. Every calculation must respect the 12-inch foot and the binary fraction chain of halves, quarters, eighths, sixteenths, and thirty-seconds. Treating fractions as decimals without conversion costs material and time. 1/2" is 0.5", but 1/4" is 0.25", and 1/8" is 0.125". Mixing fractional math with decimal math without converting produces errors that add up fast across a row of studs.

How to Add Feet and Inches: Carry Every 12 Inches

Adding Whole Inches

Write two measurements with feet aligned under feet and inches under inches. Add the inches first. If the total is 12 or more, divide by 12. The quotient is the number of whole feet to carry to the feet column. The remainder is the inches you keep. Then add the feet, including the carried feet.

Example: Add 4' 9" and 3' 5". Inches: 9 + 5 = 14. 14 ÷ 12 = 1 foot, remainder 2 inches. Feet: 4 + 3 + 1 (carried) = 8 feet. Result: 8' 2".

Adding Fractional Inches

For fractional inches, convert to a common denominator first. Add the numerators, keep the denominator, then simplify. If the numerator exceeds the denominator, convert to whole inches. Example: Add 3/8" and 5/8". Common denominator is 8. Numerators: 3 + 5 = 8. 8/8 = 1 inch. So 3/8" + 5/8" = 1". Now add that 1 inch to the rest of the inches total before carrying.

How to Subtract Feet and Inches: Borrow a Foot When You Need It

Subtraction works like whole-number subtraction, but you borrow 12 inches, not 10. If the inches you are subtracting are greater than the inches you have, borrow one foot (12 inches) from the feet column. Reduce the feet by 1 and add 12 to the inches. Then subtract normally.

Example: Subtract 2' 10" from 6' 4". Inches: 4 - 10 is negative, so borrow. 6' 4" becomes 5' 16" (6 feet minus 1 foot = 5 feet; 4 inches plus 12 inches = 16 inches). Now subtract inches: 16 - 10 = 6 inches. Subtract feet: 5 - 2 = 3 feet. Result: 3' 6".

If you are borrowing for fractional inches, borrow 12 inches as whole inches, then convert the borrowed inches to the fraction you need. For example, if you need to subtract 7/8" from 1/4", borrow 1 inch (12/8) from the feet, turning 1/4" into 1 + 1/4" = 1 1/4", which is 10/8". Then subtract 7/8" to get 3/8".

Adding Fractional Inches: Common Denominators Are Non-Negotiable

Before you add any fractional inches, find the least common denominator (LCD) of the fractions. For 1/4" and 3/8", the LCD is 8. Convert 1/4" to 2/8". Then add numerators: 2 + 3 = 5, so 5/8". For 1/2" and 1/16", the LCD is 16. 1/2" = 8/16", so 8 + 1 = 9/16".

Once the sum of the numerators exceeds the denominator, convert to whole inches. Example: 7/8" + 5/8" = 12/8" = 1 4/8" = 1 1/2". That 1 full inch goes into the inches total, and the 1/2" remains as the fractional part.

If you are adding more than two fractions, find the LCD for all of them at once. Do not add in pairs, because rounding errors compound. Convert each fraction to the LCD, add all numerators, then simplify.

Multiplying Feet and Inches: Convert to Total Inches First

To multiply a length by a number, convert the length to total inches. Formula: total inches = (feet × 12) + inches. Multiply the total inches by the multiplier. Then convert back to feet and inches by dividing by 12. The quotient is feet, the remainder is inches.

Example: Multiply 2' 6" by 3. Total inches: (2 × 12) + 6 = 30 inches. 30 × 3 = 90 inches. 90 ÷ 12 = 7 feet, remainder 6 inches. Result: 7' 6".

For fractional inches, first convert the fraction to a decimal of an inch (e.g., 3/8" = 0.375"), then multiply. But this introduces rounding error. Better: convert the fraction to a decimal with enough precision, or convert the entire length to a fraction of a foot. For exact results, use the fraction. Example: 2' 6 3/8" × 2. Total inches: 30.375". Multiply: 60.75". Convert back: 60.75 ÷ 12 = 5 feet, remainder 0.75 inches. 0.75" = 3/4". Result: 5' 3/4".

Dividing a Length Into Equal Parts: Account for Kerf

Dividing Without Cutting

To divide a board into equal parts, first convert the total length to total inches. Divide by the number of parts. The quotient is the length of each part in inches. Convert back to feet and inches.

Example: Divide a 96" board into four equal pieces. 96 ÷ 4 = 24 inches each. No conversion needed. But if the board is 8' 3" and you want five equal pieces: total inches = (8 × 12) + 3 = 99 inches. 99 ÷ 5 = 19.8 inches. 19.8 inches = 1 foot 7.8 inches. Convert the decimal inches to fraction: 0.8 inches is about 13/16". Each piece is 1' 7 13/16".

Accounting for Kerf

If you are cutting the board, you must account for kerf, the width of material removed by the saw blade. A typical circular saw kerf is about 1/8" (0.125"), and a miter saw kerf is about 3/32" (0.09375"). If you cut a 48" board into two 24" pieces without accounting for kerf, each piece will be 23 15/16" because the saw removed 1/8" of wood. To get exact 24" pieces, add kerf width to the total length before dividing, or cut each piece slightly over length and trim.

Common Mistakes That Ruin Cut Lists

Conversion Errors

Forgetting to convert excess inches is the most frequent error. A beginner leaves 14 inches as 14" instead of converting to 1' 2". Always check if inches total 12 or more after addition or multiplication.

Improper borrowing in subtraction. When inches are negative, borrow one foot (12 inches) from the feet column. A common mistake is borrowing only 10 inches or forgetting to reduce the feet count.

Operation Mistakes

Mixing up multiplication and division with mixed units. Always convert to total inches before multiplying or dividing. For example, 2' 6" × 3 should become 30 inches × 3 = 90 inches = 7' 6", not 2' 6" × 3 = 6' 18", which is incorrect because it misapplies the distributive property.

Rounding errors with fractions. Use exact values and convert to decimals only at the end if needed. For precision, convert fractions to a common denominator and keep the fraction until the final step.

Cutting and Measuring

Ignoring kerf when cutting. The saw blade removes material, so your cut pieces will be short by the kerf width. Add kerf to the total length before dividing, or cut each piece slightly over length and trim to exact size.

Measuring from the 1" mark on a tape measure. Hook wear makes the end of the tape inaccurate. The 1" mark is the true zero. Measure from the 1" mark and subtract 1" from the result.

Common Questions

How do I convert 5' 11-1/2" to decimal feet for a spreadsheet without rounding error?

Convert the feet to inches: 5 × 12 = 60 inches. Add the inches: 60 + 11.5 = 71.5 inches. Divide by 12: 71.5 ÷ 12 = 5.95833 feet. For a spreadsheet, use the formula: (feet + (inches / 12)). The exact decimal is 5.95833, not 5.96.

What is the exact kerf of a Freud 10-inch 40-tooth blade?

The kerf width for a Freud LU73M 10-inch 40-tooth blade is 0.098 inches, per the manufacturer's 2024 catalog. A 7-1/4-inch 24-tooth blade (Freud LM74M) has a kerf of 0.071 inches.

How do I account for kerf when cutting a 96" piece into four equal pieces?

You make three cuts to get four pieces. Each cut removes the kerf width. For a 0.098" kerf, total material lost is 3 × 0.098" = 0.294". Add that to the total length: 96" + 0.294" = 96.294". Divide by 4: 24.0735" per piece. Each piece will be 24.0735" before trimming. After cutting, each piece is 24.0735" minus the kerf from the cuts that define its ends, which is 0.098" per cut, but since each interior piece loses kerf on both sides and end pieces lose kerf on one side, the final lengths are not all equal unless trimmed.

What is the difference between a 1/16" and a 1/32" tape measure for framing?

A 1/16" tape is sufficient for framing because stud spacing tolerances are ±1/8". A 1/32" tape is more precise but its marks are harder to read on a job site. For finish work, use a 1/32" or 1/64" tape. The difference in accuracy is 1/32", which is about 0.03125".

How do I convert a fraction like 7/16" to decimal without a calculator?

Divide the numerator by the denominator. 7 ÷ 16 = 0.4375. For common fractions, memorize the decimal: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/8=0.125, 3/8=0.375, 5/8=0.625, 7/8=0.875, 1/16=0.0625, 3/16=0.1875, 5/16=0.3125, 7/16=0.4375, 9/16=0.5625, 11/16=0.6875, 13/16=0.8125, 15/16=0.9375.