What is a Geometry Calculator?
A geometry calculator computes the key measurements of geometric shapes — area, perimeter, circumference, surface area, and volume — using standard mathematical formulas. It covers both 2D shapes (circle, rectangle, triangle, trapezoid, parallelogram) and 3D shapes (sphere, cylinder, cone, cube, cuboid), making it useful for students, engineers, architects, and anyone working with spatial measurements.
How to Use the Geometry Calculator
Select your shape from the dropdown menu. Enter the required dimensions (radius, length, width, height, etc.) and all measurements update instantly. Units are kept consistent — if you enter dimensions in centimeters, all area results are in cm² and volume results in cm³. Simply change the shape to recalculate for a different geometry.
Formulas Used
2D Shapes:
- Circle: Area = πr²; Circumference = 2πr
- Rectangle: Area = l × w; Perimeter = 2(l + w)
- Square: Area = s²; Perimeter = 4s
- Triangle: Area = ½ × b × h; Perimeter = a + b + c
- Trapezoid: Area = ½ × (a + b) × h; Perimeter = a + b + c + d
- Parallelogram: Area = b × h; Perimeter = 2(a + b)
3D Shapes:
- Sphere: Volume = (4/3)πr³; Surface Area = 4πr²
- Cylinder: Volume = πr²h; Lateral SA = 2πrh; Total SA = 2πr(r + h)
- Cone: Volume = (1/3)πr²h; Slant height l = √(r²+h²); Lateral SA = πrl
- Cube: Volume = s³; Surface Area = 6s²
- Cuboid: Volume = l × w × h; Surface Area = 2(lw + lh + wh)
Benefits of Using a Geometry Calculator
- Instant results for all standard shapes — no formula lookup needed
- Covers both 2D and 3D geometry in one tool
- All results shown at once (area + perimeter or volume + surface area)
- Uses precise π (3.141592653589793) for accurate circle and sphere calculations
- Useful for students, home improvement planning, and engineering estimates
Frequently Asked Questions
What is the formula for the area of a circle?
Area = π × r², where r is the radius. For radius = 5: Area = π × 25 = 78.54 square units. Circumference = 2 × π × r = 31.42 units.
How do you find the area of a triangle?
Area = ½ × base × height. For base = 10, height = 6: Area = ½ × 60 = 30 square units. Height must be perpendicular to the base.
What is the formula for the volume of a cylinder?
Volume = π × r² × h. For r = 3, h = 10: Volume = π × 9 × 10 = 282.74 cubic units. Total surface area = 2πr(r + h) = 245.04 square units.
What is the difference between perimeter and area?
Perimeter = total boundary length (1D measure, e.g., meters). Area = space enclosed (2D measure, e.g., m²). A 4×3 rectangle: perimeter = 14 m, area = 12 m².
How do you calculate the volume of a sphere?
Volume = (4/3) × π × r³. For r = 5: Volume = (4/3) × π × 125 = 523.60 cubic units. Surface area = 4 × π × r² = 314.16 square units.
What is the Pythagorean theorem?
For a right triangle: a² + b² = c² (where c is the hypotenuse). To find c: c = √(a² + b²). Classic example: 3² + 4² = 9 + 16 = 25 → c = 5.
How do you find the area of a trapezoid?
Area = ½ × (a + b) × h, where a and b are the parallel sides and h is the height between them. For a = 8, b = 5, h = 4: Area = ½ × 13 × 4 = 26 square units.
What is the lateral surface area of a cone?
Lateral SA = π × r × l, where l = slant height = √(r² + h²). For r = 3, h = 4: l = √(9+16) = 5; Lateral SA = π × 3 × 5 = 47.12 square units. Volume = (1/3) × π × r² × h = 37.70 cubic units.