Feet and Inches Calculator

A length written as 5.5 ft is 5 ft 6 in. The decimal part represents half a foot, so reading it as 5 ft 5 in changes the dimension by a full inch. That distinction matters in carpentry, construction drawings, room and material measurements, and records of height.

Feet-and-inches arithmetic groups 12 inches into each foot. When adding, a full group of 12 inches carries into the feet total. For example, 4 ft 10 in plus 1 ft 5 in makes 5 ft 15 in, which becomes 6 ft 3 in. Subtraction can require borrowing one foot as 12 inches. To subtract 2 ft 7 in from 6 ft 2 in, rewrite the starting length as 5 ft 14 in, leaving 3 ft 7 in after subtraction.

Fractional inches describe the remaining part of an inch. In 3/8 in, the denominator divides an inch into eight equal parts and the numerator counts three of them. A mixed measurement such as 3 3/8 in means three whole inches plus that fraction, exactly 3.375 in. Adding unlike fractions requires a common denominator, so 3/8 in plus 1/4 in becomes 3/8 in plus 2/8 in, or 5/8 in. Writing 3.38 in changes the value because .38 means 38 hundredths of an inch.

Some calculated lengths fall between the marks available on a tape. Rounding to the nearest 1/16 in selects the closest sixteenth-inch position. A finer increment can reduce that rounding difference, but rounding an intermediate answer before multiplying or dividing again can change the final length. Keeping the full value until the final mark avoids that extra loss.

Equal spacing also requires distinguishing the clear space from the material between spaces. Three clear spaces separated by two members occupy the combined width of all three gaps and both members. A member's edge and its center are different marking positions. Measuring each cumulative position from one fixed zero edge avoids carrying a rounded gap forward from mark to mark.

Metric conversion changes the unit without changing the length. One inch is exactly 25.4 mm, and one international foot is exactly 0.3048 m. These exact definitions do not make an estimated dimension or an uncertain tape reading more accurate. Extra decimal places describe the calculation; the original measurement still determines how closely the result represents the physical object.

How to Use This Tool:

Choose the operation that matches the job, then supply only the measurements it needs. Results update as you edit.

1. Enter the Starting length, such as 5' 3 3/8", 63.375 in, 5.5 ft, or 1.6 m. A number or fraction without a unit means inches; metric entries use mm, cm, or m.
2. Choose the Operation. Add lengths and Subtract lengths use a Second length; Multiply by number and Divide by number use a unitless Number, such as 3 or 1/3. Convert length needs no second operand. For Pieces that fit, the starting length is the available stock and the second length is one piece.
   Pieces that fit does not deduct saw kerf, the material removed by a cut. A whole-piece count is a geometric fit, not a complete cutting plan.
3. Enter the Number of clear spaces for Split into equal spaces. In Advanced, keep Interior member width at 0 for plain divisions, or enter the actual width of each interior member. Reference offset starts at 0; a positive offset moves the entire layout along the same measuring reference without changing the gap size.
4. Choose Tape precision in Advanced if you need a different increment. The default is 1/16 in, with choices from 1/2 to 1/64 in. The summary badge shows the current choice even while Advanced is closed.
5. Check the answer and any marked input. If Check the measurement appears, correct the field named by the message; for a zero divisor, replace Number with a nonzero value. Valid inputs restore the answer and measurement tables.
6. Continue a calculation with Use exact result when available. It puts the unrounded answer into Starting length and selects Convert length, ready for your next operation. Split into equal spaces reuses one clear-space length, and Pieces that fit has no reuse button. Undo reuse restores the previous inputs.
   If an exact result exceeds the accepted input size for another step, the current calculation stays intact. The offered action includes its increment, such as Use rounded result (1/16 in), and deliberately adopts that tape increment, so subsequent arithmetic starts from that rounded length.

Interpreting Results:

For arithmetic, conversion, and clear spaces, the large answer is a tape-rounded representation. In Measurement equivalents, Exact inches gives the retained value and Tape rounding error shows the tape value minus the exact length. Decimal and metric equivalents come from the unrounded value. Changing Tape precision therefore changes the tape representation and its error without changing the underlying length.

• For arithmetic and conversion, Calculated length is the answer and the equivalents describe that same length.
• For Split into equal spaces, Each clear space is the gap width. The Cumulative mark list labels these Space 1 end, Member 1 end and so on, finishing with End. Member rows appear only for positive widths. These are edges, not member centers. Transfer every position from the same zero edge.
• For Pieces that fit, Whole pieces that fit is the whole-piece count. The equivalents, rounding-error badge, and chart describe the remaining length after those pieces.

Rounding error is rounded minus exact. A positive error means a higher signed value and a negative error a lower one; for positive physical lengths, these mean longer and shorter respectively. The ≈ marker appears when a nonzero quantity rounds to zero at the displayed precision: ≈0 in a decimal display or ≈0' 0" in a tape display. Check the exact value before treating it as zero.

Rounding comparison compares the current length, clear space, or remainder at all six tape increments. It does not plot every layout mark. Each cumulative position has its own error in the mark list, and very small errors may be indistinguishable from zero on the chart. Use the exact error value when that distinction matters.

Technical Details:

Mixed units become comparable when expressed in a common length unit. Finite decimals and fractions can both be retained as exact fractions of an inch, allowing arithmetic and unit conversion to finish before the result is rounded for display.

Formula Core

For feet-and-inches notation, total inches x combine the feet part F and the inches part I, including any fractional inches. Both parts are nonnegative magnitudes; s is +1 or −1 and applies to the whole length.

Let A be Starting length and B be Second length, both expressed in inches. Let k be the unitless Number. The result r remains a length under each of these operations.

Multiplying two lengths would produce area, which is outside these length operations. Dividing one length by another instead gives a dimensionless ratio, used for counting pieces.

Exact unit conversion

For x inches, an equivalent numerical value y is obtained with an exact conversion factor c. To convert an input in the other direction, divide its numerical value by the same factor.

These factors use the international foot. Historical dimensions explicitly recorded in U.S. survey feet require a different conversion factor.

Whole pieces and remainder

For a nonnegative stock length A and a positive piece length B, the whole-piece count q is the length ratio rounded down. The remaining length r is what remains after subtracting q pieces.

The remainder is at least zero and smaller than one piece. An 8 ft stock length and a 2 ft 8 in piece length give three pieces with zero remainder. All 96 inches are allocated to the pieces, leaving no material for cutting loss. The calculation does not optimize a list of different piece lengths.

Equal clear spaces and cumulative marks

A span A containing N equal clear spaces has N−1 interior members of equal actual width w. Subtract their combined width before dividing the available space. The clear-space width g must remain positive.

Here A is Starting length, N is Number of clear spaces, and w is Interior member width, with all lengths expressed in inches. Zero width gives plain equal divisions. With one space there are no interior members. End-member widths are excluded, so A must describe the span available between any end members.

For a Reference offset o, the end of clear space i is p_i. The following member ends at m_i, one member width farther along. These positions include the offset before any rounding.

Space ends run from i = 1 through N. Member ends exist only through N−1 and are listed only for positive member widths. Each absolute position is rounded independently, so a rounded gap is never repeatedly added to generate the marks.

For a 100 in span, four spaces, and three 2 in interior members, subtracting 6 in leaves 94 in for the gaps. Each gap is exactly 23.5 in. With a 1 in reference offset, the first space ends at 24.5 in, the first member ends at 26.5 in, and the final end is at 101 in. The offset moves the marks without changing the 23.5 in clear space.

These are geometric layout positions. They do not establish structural adequacy, building-code compliance, or allowances for saw cuts.

Tape rounding and decimal display

For an exact inch value x and a tape increment of 1/d in, the rounded value R_d(x) is the nearest available tick. A halfway value moves away from zero. The denominator d is 2, 4, 8, 16, 32, or 64.

The sign function supplies −1, 0, or +1; the floor brackets take the whole-number part of the nonnegative quantity inside. At a 1/16 in increment, +1/32 in rounds to +1/16 in and −1/32 in rounds to −1/16 in. Fractions are reduced after rounding, and a full 12 inches carries into the feet part.

The signed error e compares the rounded value with the exact one. Its absolute size is no more than half the selected increment.

Both e and its bound are in inches. At 1/16 in precision, the bound is 1/32 in. This describes numerical rounding only, not the uncertainty of a physical measurement.

Decimal feet, decimal inches, and metric values are separately rounded from the exact length to at most six decimal places, also with ties away from zero. Trailing zeros are removed. These displays do not establish six-place measurement accuracy, and typing a shortened decimal back into a later calculation can discard information retained by the exact fraction.

Accepted notation and calculation limits

Each measurement entry holds one length, rather than a general arithmetic expression. Feet and inches may use their unit words or symbols. In 5'-3", the hyphen after the foot marker separates feet from inches; it does not subtract. A leading minus applies to the whole measurement, so -5'-3" represents −63 in. Scientific notation, comma-formatted numbers, and yards are not accepted.

The limits below apply before an answer or a complete mark list is made available.

A further limit on layout size accounts for both fraction length and the number of marks. The number of marks M is N with zero member width, or 2N−1 with positive member width. The digit count S adds the digits in the numerators and denominators of the span and offset after exact conversion to inches and fraction reduction, ignoring signs. It also includes member width when N is greater than one, even if that width is zero.

Very long exact fractions can exceed this budget even when each measurement is valid by itself. The message asks for fewer spaces or rounded measurements before splitting. No partial mark list is returned, and a measurement that cannot be used in that layout may still be valid for ordinary arithmetic or conversion.

Privacy Notes:

The arithmetic runs locally in your browser without submitting measurements to a calculation service. Calculation does not require camera, microphone, or location access.

• Input settings can appear in the page URL. Anyone receiving a copied or shared URL may also receive those measurements and settings.
• Opening Rounding comparison loads chart resources on demand from a third-party content delivery network (CDN). If it cannot load, the exact measurements and errors remain available in Measurement equivalents.
• Copy actions use the browser's clipboard support when you request them. If copying is blocked, you can select the displayed measurement and copy it manually.

Worked Examples:

References:

• SI Units – Length, National Institute of Standards and Technology, updated September 19, 2025.
• Appendix C. General Tables of Units of Measurement, Handbook 44, National Institute of Standards and Technology, 2026.