Geometry formulas chart
A geometry formulas chart puts the perimeter, area and volume formulas in one place, like A = ½ × b × h for a triangle and V = l × w × h for a box, each with what its letters stand for.
Free printable PDF, 3rd grade to 8th grade.
One page, black and white, prints the same every time.
What is on the sheet
Perimeter
| Shape | Formula | The letters |
|---|---|---|
| Square | P = 4 × s | s = side |
| Rectangle | P = 2 × l + 2 × w | l = length, w = width |
| Triangle | P = a + b + c | a, b, c = the three sides |
| Circle | C = 2 × π × r = π × d | C = circumference, r = radius, d = diameter |
Area
| Shape | Formula | The letters |
|---|---|---|
| Square | A = s × s = s² | s = side |
| Rectangle | A = l × w | l = length, w = width |
| Parallelogram | A = b × h | b = base, h = height |
| Triangle | A = ½ × b × h | b = base, h = height |
| Trapezoid | A = ½ × (a + b) × h | a, b = the parallel sides, h = height |
| Circle | A = π × r² | r = radius, π ≈ 3.14 |
Volume
| Solid | Formula | The letters |
|---|---|---|
| Cube | V = s × s × s = s³ | s = edge |
| Rectangular prism | V = l × w × h = B × h | B = area of the base |
| Cylinder | V = π × r² × h | r = radius of the base, h = height |
| Pyramid | V = ⅓ × B × h | B = area of the base, h = height |
| Cone | V = ⅓ × π × r² × h | r = radius of the base, h = height |
| Sphere | V = 4/3 × π × r³ | r = radius |
Reading the formulas
Perimeter is the distance around a flat shape, so it is measured in units, like inches. Area is the space inside it, in square units. Volume is the space inside a solid, in cubic units. The small 2 and 3 in the formulas match those units: s² is in square units and s³ in cubic ones.
Some formulas come in pairs. A triangle has half the area of a parallelogram with the same base and height, and a cone or pyramid holds a third of the cylinder or prism with the same base and height. Learning the pairs is easier than learning each formula on its own.
Which grade uses which
Third grade finds the area and perimeter of rectangles (CCSS 3.MD.C.7 and 3.MD.D.8), and 4th grade uses the formulas (4.MD.A.3). Fifth grade finds the volume of a rectangular prism (5.MD.C.5). Sixth grade finds the area of triangles, parallelograms and trapezoids (6.G.A.1), 7th grade works with circles (7.G.B.4), and 8th grade with cylinders, cones and spheres (8.G.C.9).
Common questions
- Why is the area of a triangle half of base times height?
- Two copies of the same triangle fit together into a parallelogram with the same base and height. The parallelogram's area is b × h, so one triangle is half of that.
- What is π?
- π, or pi, is the distance around any circle divided by the distance across it. It is a little more than 3, and 3.14 is close enough for most school problems.