How this tool fits your workflow
Geometry in the real world
Calculating area and volume is essential for construction, manufacturing, landscaping, and design. A contractor needs the area of a room to estimate flooring costs. A painter needs the area of walls to calculate paint required. A farmer needs the area of a field to determine seeding rates and irrigation needs.
Volume calculations determine material quantities: concrete for a cylindrical foundation, gravel for a conical pile, water for a spherical tank. Shipping and storage depend on volume—calculate how many items fit in a container or how much liquid a tank holds.
Area formulas for common shapes
Circle: pi times r^2. Rectangle: length times width. Triangle: (1/2) times base times height. Trapezoid: (1/2) times (a + b) times height where a and b are parallel sides. Parallelogram: base times perpendicular height. Ellipse: pi times a times b where a and b are the semi-major and semi-minor axes.
For irregular shapes, approximate by dividing into known shapes and summing areas. For shapes defined by coordinates, the shoelace formula computes exact area from vertex coordinates. This calculator shows each formula so you can verify inputs match your physical measurements.
Volume formulas for common solids
Cube: s^3. Cuboid: l times w times h. Sphere: (4/3) times pi times r^3. Cylinder: pi times r^2 times h. Cone: (1/3) times pi times r^2 times h. Pyramid: (1/3) times base area times h.
Practical uses: calculating concrete for a cylindrical column, paint for a spherical tank, or gravel for a conical pile. The calculator displays the formula so you can verify inputs match your physical measurements.
Instant calculations in your browser
Calculate area and volume on a job site, in a classroom, or at home without uploading measurements to a server. Supports metric and imperial units so you can work in feet and inches or meters and centimeters seamlessly.
Frequently asked questions
- What is the formula for the area of a circle?
- Area = pi times r^2, where r is the radius. For radius 5: area = 3.14159 times 25 = 78.54 square units. If you know the diameter, radius = diameter divided by 2.
- What is the formula for the volume of a sphere?
- Volume = (4/3) times pi times r^3. For radius 3: volume = (4/3) times 3.14159 times 27 = 113.1 cubic units.
- How do I calculate the area of a triangle?
- Area = (1/2) times base times height, where height is perpendicular to the base. With three side lengths, use Heron's formula: s = (a+b+c)/2, area = sqrt(s(s-a)(s-b)(s-c)).
- What units does the calculator use?
- Enter measurements in any consistent unit (meters, feet, inches). The result is in square units for area and cubic units for volume, matching whatever unit you used.