Feet and Inches Fraction Calculator

This calculator converts measurements in feet and inches, including fractional inches, into a single decimal value in feet or inches, and can also convert decimal feet back into feet-inches-fraction format. You enter a value like 5 ft 6 3/4 in, and it returns the equivalent in decimal feet (5.5625 ft) and decimal inches (66.75 in), plus the reverse conversion. It handles fractions with denominators up to 32, which covers most construction and woodworking needs.

Formula

The core formula converts a mixed measurement (feet, inches, and a fraction of an inch) into a single decimal number. Let:

• F = whole feet
• I = whole inches
• n/d = fractional inch (e.g., 3/4)

Then:

Decimal feet = F + (I + n/d) / 12

Decimal inches = I + n/d + F × 12

To go the other way, take the decimal feet, subtract the whole feet, multiply the remainder by 12 to get inches, and then convert the fractional part of the inch to the nearest fraction with your chosen denominator.

Worked Example

Using the default values from the calculator above: 5 feet, 6 inches, and 3/4 inch (denominator 4).

1. Convert the fraction to decimal: 3 ÷ 4 = 0.75 inches.
2. Total inches = 6 + 0.75 = 6.75 inches.
3. Convert to decimal feet: 5 + (6.75 / 12) = 5 + 0.5625 = 5.5625 ft.
4. Decimal inches = 6.75 + 5 × 12 = 6.75 + 60 = 66.75 in.

The calculator displays 5.5625 ft and 66.75 in, matching the steps above.

Why Use Feet and Inches Fractions?

The imperial system still dominates construction, carpentry, and interior design in the United States. Lumber is sold in nominal sizes like 2×4, but actual dimensions are often fractional (e.g., 1.5 in × 3.5 in). When you measure a wall, you might get 12 ft 7 5/8 in. Doing arithmetic with fractions by hand is error-prone, especially when you need to add, subtract, or multiply measurements. A calculator that handles the fraction for you reduces mistakes and speeds up estimating material quantities, cutting boards, or fitting furniture.

How to Read the Results

The first output, Decimal feet, is the total length expressed as a single number of feet. For example, 5 ft 6 3/4 in becomes 5.5625 ft. This is useful when you need to multiply by a price per foot or convert to metric (multiply by 0.3048 to get meters).

The second output, Decimal inches, is the total length in inches. The same measurement is 66.75 in. This is handy when working with inch-based products like pipes or bolts.

The third output, Feet and fraction, repeats the input in a normalized format. It shows that 5 ft 6 3/4 in is exactly that, not a rounded version. If you enter a fraction with a denominator that doesn’t divide evenly, the calculator will round to the nearest fraction with the denominator you chose.

Common Mistakes and How to Avoid Them

• Mixing feet and inches in one number: 5.6 ft is not the same as 5 ft 6 in. Always separate whole feet from inches.
• Forgetting to reduce fractions: 2/4 is the same as 1/2, but some calculators may show 2/4. This calculator keeps the denominator you enter, so enter the fraction in simplest form if you want a clean result.
• Using 12 inches per foot incorrectly: There are 12 inches in a foot, so 6 inches is 0.5 ft, not 0.6 ft.
• Rounding too early: If you round intermediate results, the final answer can be off by a noticeable amount. Do all calculations with full precision, then round only the final answer.

Limits of the Formula

This calculator assumes a standard 12-inch foot and a decimal representation of fractions. It does not handle unusual units like survey feet (which are slightly different) or metric conversions automatically. It also does not account for material shrinkage, cutting kerf (the width of a saw blade), or waste. For a real project, you should add extra material for mistakes and offcuts—typically 10% for lumber, but that depends on the project.

Alternatives and Related Tools

If you need to add or subtract multiple measurements, you can use this calculator repeatedly, but a dedicated construction calculator that handles feet, inches, and fractions in a single expression is more efficient. Many smartphone apps and physical construction calculators offer that. For metric users, the equivalent is a simple decimal calculator, since centimeters and millimeters are already decimal. For quick mental math, remember that 1 inch = 2.54 cm exactly, and 1 foot = 0.3048 m.

Frequently Asked Questions

How do I convert 5 ft 6 3/4 in to just inches?

Multiply the feet by 12 (5 × 12 = 60), add the whole inches (6) to get 66, then add the fraction (0.75) to get 66.75 inches. The calculator does this instantly.

Can this calculator handle negative measurements?

Yes, the inputs allow negative values, but the fraction input is limited to non-negative numbers. If you need to represent a negative distance, put the minus sign on the feet or inches field, not the fraction.

What if my fraction has a denominator like 16 or 32?

Enter the denominator in the “Fraction denominator” field. The calculator will use that denominator for the fraction input. For example, 5 ft 6 3/16 in requires denominator 16.

Why does the decimal feet result have four decimal places?

Four decimal places in feet corresponds to about 0.003 inches, which is far more precise than typical construction tolerances (usually 1/16 inch). The extra digits help when you need to convert to metric or do further calculations.

Is there a way to convert decimal feet back to feet and inches?

Yes. Take the decimal feet, subtract the whole number, multiply the remainder by 12 to get inches. Then convert the fractional inch to your desired fraction. For example, 5.5625 ft → 0.5625 × 12 = 6.75 in → 6 3/4 in.

Related

• Diameter x Height Volume Calculator: How It Works
• Cubic Feet Calculator: How to Find Volume
• Degrees to Meters Calculator: Convert Angles to Distance

in ft | Feet | ft | 5 | 0
in inch | Inches | in | 6 | 0
in frac | Fraction of inch | - | 0.75 | 0
in denom | Fraction denominator | - | 4 | 1
out dec_ft | Decimal feet | ft | ft + (inch + frac) / 12 | 4
out dec_in | Decimal inches | in | inch + frac + ft * 12 | 2
out frac_ft | Feet and fraction | ft-in | (ft + (inch + frac) / 12) | 4