How to Add or Subtract Feet and Inches
Here are the steps to adding or subtracting feet and inch measurements.
Step #1: First feet and inch measurement: Convert the feet to inches and the inches to decimal inches, then add the feet and decimal inches to get the total decimal inches.
Step #2: Second feet and inch measurement: Convert the feet to inches and the inches to decimal inches, then add the feet and decimal inches to get the total decimal inches.
Step #3: Perform the operation on the two decimal inch totals from Steps #1 and #2.
Step #4: Convert the result in Step #3 back to feet and inches.
4a: Divide the result from Step #3 by 12 (inches/foot) and round that result down to the nearest whole number. This becomes the "feet" portion of feet and inches result.
4b: Multiply the feet portion of the measurement (result from 4a) by 12 and subtract that result from the total decimal inches to get the inches portion of the measurement.
This leaves you with the decimal feet and inches resulting from the addition or subtraction.
Step #5 (optional): Convert the decimal feet and inches to tape measure feet and inches.
5a: The feet portion and whole-inch portion of the decimal feet and inches result remain the same for the tape measure result.
5b: To convert the fractional portion of the decimal inches result to tape measure fractional inches, you multiply the fractional decimal inches by the denominator portion of the rounding value you selected (16 if rounding to 1/16), and then round that result to the nearest whole number which then becomes the numerator of the fractional inch (if the rounded result is 11, and rounding to nearest 16th, the fraction tape measure inch would be 11/16).
5c: If the numerator and denominator from 5b have a common factor greater than 1, divide the numerator and denominator by their greatest common factor to get the reduced fractional inch.
The above 5 steps will leave you with the feet and inches result from adding or subtracting in both decimal and tape measure formats.
Example of How to Add Feet and Inches
Add 6 feet 5 1/4 inches to 3 feet 2 7/8 inches
Step #1: Convert 6' 5 1/4" to decimal inches.
Convert 6' to decimal inches. Since 6 is already in decimal format, multiply 6 by 12 to get 72 decimal inches.
Convert 5 1/4" to decimal inches. Convert the mixed number 5 1/4 to a decimal. To do that, we multiply the denominator 4 by the whole number 5 and then add that result (20) to the numerator 1 to get the new numerator 21. From there, we divide the new numerator by the denominator to get the decimal 5.25 (5 1/4 = 21/4 = 5.25).
Add the feet decimal inches (72) to the inch decimal inches (5.25) to get 77.25 total decimal inches for 6' 5 1/4" .
Step #2: Convert 3' 2 7/8" to decimal inches.
Convert 3' to decimal inches. Since 3 is already in decimal format, multiply 3 by 12 to get 36 decimal inches.
Convert 2 7/8" to decimal inches. Convert the mixed number 2 7/8 to a decimal. To do that, we multiply the denominator 8 by the whole number 2 and then add that result (16) to the numerator 7 to get the new numerator 23. From there, we divide the new numerator by the denominator to get the decimal 2.875 (2 7/8 = 23/8 = 2.875).
Add the feet decimal inches (36) to the inch decimal inches (2.875) to get 38.875 total decimal inches for 3' 2 7/8" .
Step #3: Perform the addition.
Add the first total decimal inches (77.25) to the second total decimal inches (38.875) to get 116.125 total decimal inches.
Step #4: Convert the total decimal inches (116.125) to feet and inches.
Divide 116.125 by 12 (inches) to get 9.6771 decimal feet.
Round 9.6771 down to the nearest whole number to get the feet portion of the measurement (9).
Multiply the feet portion of the measurement (9) by 12 and subtract that result (108) from the total decimal inches (116.125) to get the inches portion of the measurement (8.125).
The decimal inches (116.125) have now been converted to 9' 8.125".
Step #5: Convert the decimal feet and inches (9' 8.125") to tape measure feet and inches.
The feet portion and whole-inch portion of the decimal feet and inches result remain the same for the tape measure result (9 feet, 8 inches).
To convert the fractional portion of the decimal feet and inches result (0.125) to tape measure fractional inches, you multiply the 0.125 by the denominator portion of the rounding value you selected (1/16), and then round that result (0.125 x 16 = 2) to the nearest whole number (2). This becomes the numerator of the fractional inch (2/16).
However, since the numerator and denominator of (2/16) have a common factor greater than one (2), divide the numerator and denominator by 2 to get a reduced fractional inch of 1/8.
The decimal feet and inches (9' 8.125") have now been converted to a 9' 8 1/8" tape measurement.
Example of How to Subtract Feet and Inches
Subtract 3 feet 2 7/8 inches from 6 feet 5 1/4 inches
Step #1: Convert 6' 5 1/4" to decimal inches.
Convert 6' to decimal inches. Since 6 is already in decimal format, multiply 6 by 12 to get 72 decimal inches.
Convert 5 1/4" to decimal inches. Convert the mixed number 5 1/4 to a decimal. To do that, we multiply the denominator 4 by the whole number 5 and then add that result (20) to the numerator 1 to get the new numerator 21. From there, we divide the new numerator by the denominator to get the decimal 5.25 (5 1/4 = 21/4 = 5.25).
Add the feet decimal inches (72) to the inch decimal inches (5.25) to get 77.25 total decimal inches for 6' 5 1/4" .
Step #2: Convert 3' 2 7/8" to decimal inches.
Convert 3' to decimal inches. Since 3 is already in decimal format, multiply 3 by 12 to get 36 decimal inches.
Convert 2 7/8" to decimal inches. Convert the mixed number 2 7/8 to a decimal. To do that, we multiply the denominator 8 by the whole number 2 and then add that result (16) to the numerator 7 to get the new numerator 23. From there, we divide the new numerator by the denominator to get the decimal 2.875 (2 7/8 = 23/8 = 2.875).
Add the feet decimal inches (36) to the inch decimal inches (2.875) to get 38.875 total decimal inches for 3' 2 7/8" .
Step #3: Perform the subtraction.
Subtract the second total decimal inches (38.875) from the first total decimal inches (77.25) to get 38.375 total decimal inches.
Step #4: Convert the total decimal inches (38.375) to feet and inches.
Divide 38.375 by 12 (inches) to get 3.1979 decimal feet.
Round 3.1979 down to the nearest whole number to get the feet portion of the measurement (3).
Multiply the feet portion of the measurement (3) by 12 and subtract that result (36) from the total decimal inches (38.375) to get the inches portion of the measurement (2.375).
The decimal inches (38.375) have now been converted to 3' 2.375".
Step #5: Convert the decimal feet and inches (3' 2.375") to tape measure feet and inches.
The feet portion and whole-inch portion of the decimal feet and inches result remain the same for the tape measure result (3 feet, 2 inches).
To convert the fractional portion of the decimal feet and inches result (0.375) to tape measure fractional inches, you multiply the 0.375 by the denominator portion of the rounding value you selected (1/16), and then round that result (0.375 x 16 = 6) to the nearest whole number (6). This becomes the numerator of the fractional inch (6/16).
However, since the numerator and denominator of (6/16) have a common factor greater than one (2), divide the numerator and denominator by 2 to get a reduced fractional inch of 3/8.
The decimal feet and inches (3' 2.375") have now been converted to a 3' 2 3/8" tape measurement.