Radius stairs

[RaymondB]

I'd like to build keystone block steps up a short slope in my yard. I would like to use a design where each step is an arc or radius. I know how to calculate the length of the arc if I am using a half circle but I dont know how to calculate if I am using less than half. For example, if I draw a diameter line across a circle I have cut the circle in half. Now if I take that stright diameter line and move toward the edge (the line is then called a chord) I now have a smaller section of circle. How do I calculate the length of the arc on the smaller circle section. (I knew I should have paid more attention in math class). Any help or links to help would be appreciated.

[Richard A Hetzel]

You would need to know the angle which intersects the chord and the center of the circle, which will be an Isosceles traingle. If your chord is x and your radius is y, then the sides of the triangle are x, y and y. Once you have calculated the angle at the center, divide that by 360, and multiply that answer (it will be a decimal) by the circumference of the circle, and you wioll have your arc length.

[Joe Bartok]

I'd like to build keystone block steps up a short slope in my yard. I would like to use a design where each step is an arc or radius. I know how to calculate the length of the arc if I am using a half circle but I dont know how to calculate if I am using less than half. For example, if I draw a diameter line across a circle I have cut the circle in half. Now if I take that stright diameter line and move toward the edge (the line is then called a chord) I now have a smaller section of circle. How do I calculate the length of the arc on the smaller circle section. (I knew I should have paid more attention in math class). Any help or links to help would be appreciated.
If you have a scientific calculator set the angle mode to "Radians" (or "RAD" ... there's a button marked DRG → Degrees/Radians/Grads). Either of the following formulas will solve the arc length ...

Length of Arc = 2 × Radius × arcsin(½ Chord/Radius)
Length of Arc = Diameter × arcsin(Chord/Diameter)

The arcsine is generally labelled as "sin–¹" on a calculator and called using the "2ndF" key. Here is a link to some circle math and Javascript circle calculators (http://ca.geocities.com/web_sketches/circle_calculators/CIRCLE_SOLVER.html) to double check your numbers. Specifically, try the Sagitta Calculator (http://ca.geocities.com/web_sketches/circle_calculators/SAGITTA.html). Enter your arc length and chord; if you have calculated the arc length correctly the script will back calculate the radius of your circle.