Offsets, angles, and bends

Why it matters

Conduit, pipe and tubing rarely run in perfectly straight lines. When a run of electrical conduit needs to step around a beam, a pipe or a box, the electrician bends an offsetTwo equal bends that shift conduit sideways around an obstacle and then continue in the original direction.: two equal bends that shift the conduit sideways and then continue in the original direction. Getting the marks right first time saves material and time, and it is one of the most visible signs of skill on a job site. The math behind it is basic right-triangle trigonometry, and the same ideas help mechanics with angles, slopes and shims.

Core idea: the offset is a right triangle

Picture the conduit stepping over an obstacle. The two bends at angle theta form a right triangle:

• The offset depth (how far the conduit must move sideways) is the side opposite the angle.
• The distance between bends (along the conduit, from one bend mark to the other) is the hypotenuseThe longest side of a right triangle; in an offset, the distance between the bend marks..

From trigonometry, sin(theta) = opposite / hypotenuse. Rearranged:

distance between bends = offset depth / sin(theta)

The number 1 / sin(theta) is called the multiplier1 / sin(angle), the number you multiply the offset depth by to get the distance between bends. (or cosecant). Trade tables list it so you can just multiply.

Worked example 1: a 6 inch offset with 30 degree bends

• Offset depth = 6 in.
• sin(30 degrees) = 0.5, so the multiplier is 2.
• Distance between bends = 6 / 0.5 = 12 in.

So the two bend marks go 12 inches apart.

Worked example 2: a 10 inch offset with 45 degree bends

• sin(45 degrees) = 0.7071.
• Distance between bends = 10 / 0.7071 = 14.14 in.
• To the nearest sixteenth: 0.14 x 16 = 2.3, which rounds to 2, so 2/16 = 14 1/8 in.

Shrink

Because the conduit now travels diagonally for part of its length, an offset "uses up" a little extra conduit compared with a straight run. This lost length is called shrink. The exact geometry gives:

shrink = offset depth x tan(theta / 2)

For the 6 in offset at 30 degrees: 6 x tan(15 degrees) = 6 x 0.268 = 1.61 in. The trade-table shortcut of 1/4 in per inch of offset gives 6 x 1/4 = 1 1/2 in, close enough for most work with a hand bender. Your instructor will show how your bender and your crew apply shrink when marking a stick, because the marking conventions depend on the bender and the direction you bend.

Choosing the angle

• Smaller angles (10 or 22.5 degrees) make gentler bends that are easier to pull wire through, but they need more distance between bends.
• Larger angles (45 or 60 degrees) fit tight spaces but add more resistance to the wire pull.

The code also limits the total degrees of bends between pull points (in the US, 360 degrees between pull points for most conduit types). An offset with two 30 degree bends uses 60 of those degrees.

Converting angles for JavaScript

Calculators and programming languages compute sine with angles in radiansThe angle unit Math.sin expects; radians = degrees x pi / 180., not degrees. To convert: radians = degrees x pi / 180. In JavaScript:

const radians = 30 * Math.PI / 180;      // 0.5236
console.log(Math.sin(radians));          // 0.5 (very close to it)

Forgetting this conversion is the most common bug in trade calculators: Math.sin(30) treats 30 as radians and returns -0.988.

Worked example 3: checking a field measurement

An apprentice wants a 4 in offset with 22.5 degree bends and wonders whether 10 1/2 in between bends is right.

• sin(22.5 degrees) = 0.3827. Distance = 4 / 0.3827 = 10.45 in.
• To the nearest sixteenth: 0.45 x 16 = 7.2, rounds to 7, so 10 7/16 in.

10 1/2 in (10 8/16) is 1/16 in long: a small but real difference on a tight offset.

Common mistakes

• Using cosine or tangent instead of sine for the distance between bends. Remember: depth is opposite, distance is the hypotenuse.
• Degrees versus radians in calculators and code.
• Unequal bends. Both bends of an offset must be the same angle, or the conduit will not come back parallel.
• Dog legsA twist in conduit caused by two bends that are not in the same plane.. If the two bends are not in the same plane, the conduit twists. Sight down the conduit after bending.
• Practising on the wrong things. Bending practice belongs in a shop or apprenticeship lab with proper benders and supervision. At home, practise the math on paper.

Try it

Open the Do tab. The offset calculator already converts degrees to radians, computes shrink, and rounds to the nearest sixteenth. You write the one line that computes the distance between bends.

Quick recap

• An offset is a right triangle: depth is opposite, distance between bends is the hypotenuse.
• Distance between bends = depth / sin(angle); the multiplier is 1 / sin(angle).
• Shrink = depth x tan(angle / 2); trade tables round it per inch of offset.
• Convert degrees to radians before using Math.sin.