Determine Radius

For this exercise we will determine the the RADIUS of an arc if we know the RISE and the CHORD.

In this exercise we will take a 36 inch long ruler (Line “B – “C”) and place it across the arc. The ruler must be straight and both ends of the ruler must be touching the arc. Any length ruler or straight edge will do, just as long as you know its length and where its midpoint is.

Now measure the vertical height (Line “A” – “D”) at the halfway point of line “B – “C” (Point “D”) which is at the 18 inch mark of the ruler. The height in this case will be 1.25 inches.

On your calculator punch in 1.25 ÷ by 18 = you get .06944. Now hit INV or on some calculators 2nd. Now punch in TAN x 2 = You get 7.945
Now hit SIN then the key 1/x You should have 7.2347  Now x 18 = You get 130.225.
The RADIUS of this arc is 130.23 inches.

In short:

Rise ÷ (1/2 of chord) =____ INV or 2nd TAN x 2 = ____ SIN 1/X  x  (1/2 of chord) = RADIUS

This exercise is good for all arcs of less than 180 degrees of arc.