Carpentry Math
The carpentry math, used for most projects, can be narrowed
down to some basic formulas and computations provided right here on this page.
The formulas below can be used to square a wall or deck frame (the
Pythagorean Theorem), calculate the area of a circle, calculate
the volume of a cylinder, calculate
the circumference of a circle, and more.
Right Triangles  The Pythagorean Theorem
The Pythagorean theorem is used extensively in carpentry and
construction. Almost every carpentry project involves some
combination of squares and triangles.
The square of the hypotenuse of a right triangle is equal to
the sum of the squares of the other two sides. The square
of side A plus the square of side B equals the square of side C.
A^{2} + B^{2} = C^{2}
The square of one side of a right triangle equals the square
of the hypotenuse minus the square of the other side. The
length of the square of side A equals the square of side C minus
the square of side B.
A^{2} = C^{2}  B^{2}


If this sounds complicated, consider
the 345 rule of a righttriangle. It is the best
way to square two walls. Here's how it works  if one side of a
righttriangle is three feet and the other side is four feet
and the hypotenuse (or long side of the triangle) is five feet, then angle 'A'
is 90 degrees (see diagram at right). If you
want to square something larger, you can use proportions
of this same formula, such as 6810.
5^{2} = 4^{2} + 3^{2} or
10^{2} = 8^{2} +
6^{2}



How to calculate the square feet of a triangle 
The area of a triangle is equal to onehalf the
product of the base and height.
A = .5 x (B x H)



How to calculate the area of a rectangle 
To calculate the area of a rectangle,
simply multiply the length of side 1 by the length of side 2.
A = S_{1} x S_{2}



How to calculate the area of a trapezoid

To calculate area of a trapezoid, multiply its
height by onehalf the sum of the parallel sides.
A = .5 x (L_{1} + L_{2}) x H



Calculate area of a circle 
To calculate the area of a circle, multiply the
circumference by onehalf the radius.
A = C x .5(R)
Or, multiply the
radius^{2} by 3.1416 (pi).
A = 3.1416 x R^{2}



How to calculate circumference of a circle 
To calculate the circumference of a
circle, multiply the diameter by 3.1416 (pi).
C = 3.1416 x D



How to calculate the volume of a cylinder 
To calculate the volume of a cylinder,
multiply the radius squared x 3.1416 (pi) x the height of the
cylinder.
V = 3.1416 x R^{2} x H


If you know of any other formulas that you would like to see added to
this carpentry math page, please
contactus.
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