Stadia Distance Calculator

It is a way to measure distance with a telescope that carries two horizontal cross hairs, the stadia hairs. The length of rod that appears between those hairs grows in proportion to how far away the rod stands, so reading the intercept gives you distance without stretching a tape.

K is the multiplying constant, almost always 100 on a modern instrument, and C is the additive constant, usually 0 because the lens system is internally focusing. For a level sight the distance is simply K times the intercept plus C, so a 1.5 ft intercept at K 100 reads 150 ft.

It uses the standard reduction formulas. Horizontal distance is K times the intercept times the cosine of the angle squared, plus C times the cosine. Vertical distance is K times the intercept times the sine times the cosine, plus C times the sine. At an angle of zero these collapse back to K times the intercept.

It is the rise or fall from the horizontal axis of the instrument to the point you sighted on the rod, not the elevation of the ground. A positive angle produces a rise and an equal negative angle produces a fall of the same size, which is why the 5 degree and -5 degree cases mirror each other.

It works in feet. Enter the rod intercept in feet and both distances come back in feet. If you read the rod in another unit, convert the intercept first, since the result carries whatever length unit you feed the interval.

The interval is a measured length of rod between the two hairs, so a value of zero or below has no physical meaning and is rejected. The multiplying constant K must also be positive for the same reason.

The vertical angle must sit between -90 and 90 degrees, not including the ends. A sight straight up or straight down would drive the horizontal distance to zero and is outside the practical range of a stadia reading, so the tool blocks it.

Yes. The reduction runs entirely in your browser with plain trigonometry, and nothing you type is uploaded or stored. You can use it on a field laptop with no connection.

Modern total stations and GPS are faster and more precise, so stadia is rarely the first choice on a paid job. It remains useful for teaching, for rough checks, and for reducing old field notes that were recorded with a transit and stadia rod.