What this converter does
This tool converts a height given in centimeters into US customary units: decimal inches, decimal feet, and the everyday feet-and-inches form (like 5 ft 6 7/8 in). Because the conversion uses the exact international inch (1 inch = 2.54 cm exactly), it is pure unit conversion and gives identical results everywhere in the world.
How to use it
Enter your height in centimeters. Then choose the fraction precision for the feet-and-inches answer by typing a denominator after "1/" — for example 8 rounds the leftover inches to the nearest 1/8 inch, 16 to the nearest 1/16, and so on. Press calculate to see all four results. The displayed fraction is automatically reduced (so 4/8 shows as 1/2).
The formula explained
Decimal inches = cm / 2.54. Decimal feet = inches / 12 (equivalently cm / 30.48, since one foot is 30.48 cm). For the combined form, whole feet is the floor of inches / 12. The leftover inches (a value between 0 and 12) are split into a whole-inch part and a fractional part. The fraction is found by rounding (frac \(\times\) D) to the nearest whole numerator over your chosen denominator D, then reducing by the greatest common divisor. If rounding pushes the inches to 12, it rolls over into an extra foot.
$$\text{inches} = \frac{\text{cm}}{2.54}, \quad \text{feet} = \frac{\text{cm}}{30.48}$$$$\text{ft} = \left\lfloor \frac{\text{in}}{12} \right\rfloor, \quad \text{frac} = \frac{\text{round}((\text{in} \bmod 12 - \lfloor \rfloor)\cdot D)}{D}$$
Worked example
For 170 cm with denominator 8: decimal inches = 170 / 2.54 = 66.93 in; decimal feet = 66.93 / 12 = 5.58 ft. Whole feet = floor(5.5774) = 5, leftover = 6.929 in. Whole inch part = 6, frac = 0.929, numerator = round(0.929 \(\times\) 8) = 7, giving 7/8. Result: 5 ft 6 7/8 in.
$$\text{inches} = \frac{170}{2.54} = 66.93 \text{ in}$$$$\text{feet} = \frac{66.93}{12} = 5.58 \text{ ft}$$$$\text{round}(0.929 \times 8) = 7$$
FAQ
Is the conversion exact? Yes. The international inch is defined as exactly 2.54 cm, so the math is exact and locale-independent.
Why choose a denominator? Tape measures and rulers come in fractional gradations (halves, quarters, eighths, sixteenths). Picking the matching denominator gives a number you can read straight off a real ruler.
What about 0 or negative input? Zero centimeters returns 0 in / 0 ft / 0 ft 0 in. Negative heights are treated as 0 because a height cannot be negative.
