Compass (Drawing Tool) — Definition, Formula & Examples

A compass is a hinged drawing tool with a pointed end and a pencil end, used to draw circles, arcs, and mark off equal distances in geometric constructions.

A compass is a geometric instrument consisting of two arms joined at a pivot: one arm terminates in a sharp point that serves as a fixed center, and the other holds a marking implement. By rotating the marking arm around the fixed point at a constant radius, the compass traces a circle or circular arc in the plane.

How It Works

Place the pointed end of the compass on your paper where you want the center of the circle. Spread the arms apart until the pencil end is at the desired radius — you can measure this distance against a ruler. Hold the top of the compass and rotate it steadily, keeping the point firmly in place. The pencil traces a perfect circle. For constructions like bisecting a segment, you swing short arcs from two different center points and mark where they intersect.

Worked Example

Problem: Use a compass to construct an equilateral triangle with side length 5 cm.

Step 1: Draw a base segment AB that is 5 cm long using a straightedge and ruler.

AB = 5 \text{ cm}

Step 2: Set your compass width to 5 cm. Place the compass point on A and draw an arc above the segment.

Step 3: Without changing the compass width, place the point on B and draw another arc that crosses the first arc. Label the intersection point C.

Step 4: Connect A to C and B to C with straight lines. Since AC = BC = AB = 5 cm, triangle ABC is equilateral.

AC = BC = AB = 5 \text{ cm}

Answer: Triangle ABC is an equilateral triangle with all sides equal to 5 cm and all angles equal to 60°.

Why It Matters

Compass-and-straightedge constructions are central to Euclidean geometry and teach precise reasoning without measurement shortcuts. These skills appear in middle school and high school geometry courses, and they build the spatial thinking used in drafting, architecture, and engineering design.

Common Mistakes

Mistake: Letting the compass slip or change width while drawing an arc.

Correction: Hold the compass firmly at the top and press the point into the paper slightly. Tighten the hinge so the arms stay at the set width throughout the arc.