Square Pyramid Calculator (Volume & Surface Area)
Square Pyramid Calculator (Volume & Surface Area)
A square pyramid has a square base and four triangular faces that meet at a single apex directly above the base's center - the Great Pyramid of Giza is the most famous real-world example. Enter the base side length and the vertical height (in whatever unit you like), and this calculator finds the slant height (the distance from the middle of a base edge up to the apex), the volume, and both the lateral and total surface area, along with a diagram and the full step-by-step working.
- V = ⅓b²h, exactly one-third of a rectangular box with the same base and height - a pyramid with a 6-unit base and height 4 has a volume of ⅓ × 6² × 4 = 48 cubic units.
- The slant height is l = √(h² + (b/2)²), found with the Pythagorean theorem using the height and half the base - for base 6 and height 4, that's √(16+9) = √25 = 5, another 3-4-5 triangle.
- Total SA = b² + 2bl adds the square base to the four triangular faces (each with area ½ × b × l, so 4 of them give 2bl) - for base 6, height 4 (slant 5), that's 36 + 60 = 96 square units.
How do I find the volume of a square pyramid?
Use V = ⅓b²h, where b is the base side and h is the vertical height. A pyramid with base 6 and height 4 has a volume of ⅓ × 36 × 4 = 48.
What is the slant height of a pyramid?
It's the distance from the midpoint of a base edge up to the apex, found with l = √(h² + (b/2)²) - not the same as the height, which goes straight up from the base's center.
Square Pyramid Calculator (Volume & Surface Area)
A square pyramid has a square base and four triangular faces that meet at a single apex directly above the base's center - the Great Pyramid of Giza is the most famous real-world example. Enter the base side length and the vertical height (in whatever unit you like), and this calculator finds the slant height (the distance from the middle of a base edge up to the apex), the volume, and both the lateral and total surface area, along with a diagram and the full step-by-step working.
- V = ⅓b²h, exactly one-third of a rectangular box with the same base and height - a pyramid with a 6-unit base and height 4 has a volume of ⅓ × 6² × 4 = 48 cubic units.
- The slant height is l = √(h² + (b/2)²), found with the Pythagorean theorem using the height and half the base - for base 6 and height 4, that's √(16+9) = √25 = 5, another 3-4-5 triangle.
- Total SA = b² + 2bl adds the square base to the four triangular faces (each with area ½ × b × l, so 4 of them give 2bl) - for base 6, height 4 (slant 5), that's 36 + 60 = 96 square units.
How do I find the volume of a square pyramid?
Use V = ⅓b²h, where b is the base side and h is the vertical height. A pyramid with base 6 and height 4 has a volume of ⅓ × 36 × 4 = 48.
What is the slant height of a pyramid?
It's the distance from the midpoint of a base edge up to the apex, found with l = √(h² + (b/2)²) - not the same as the height, which goes straight up from the base's center.