Right Square Pyramid Calculator
Calculate area (A), lateral area (A_l), volume (V), and face area (A_f) of a right square pyramid
Enter Pyramid Dimensions
Enter any two dimensions to calculate all pyramid properties
Side length of the square base
Vertical height from base to apex
Height of triangular face from base to apex
Edge from base corner to apex
Diagonal of the square base (diagonal = a√2)
Calculated Dimensions
Area and Volume Results
Example Calculation
Square Pyramid with Base Edge = 6 units, Height = 4 units
Given: Base edge (a) = 6 units, Height (H) = 4 units
Step 1: Calculate slant height: s = √(H² + (a/2)²) = √(4² + 3²) = √25 = 5 units
Step 2: Calculate base area: A_b = a² = 6² = 36 sq units
Step 3: Calculate lateral face area: A_f = (a × s)/2 = (6 × 5)/2 = 15 sq units
Step 4: Calculate total lateral area: A_l = 4 × A_f = 4 × 15 = 60 sq units
Step 5: Calculate total surface area: A = A_l + A_b = 60 + 36 = 96 sq units
Step 6: Calculate volume: V = (A_b × H)/3 = (36 × 4)/3 = 48 cubic units
Right Square Pyramid Properties
Square base with four triangular faces
Apex directly above the center of the base
All lateral faces are congruent isosceles triangles
Base has 4 right angles (90°)
All other angles are acute
Key Formulas
Slant Height
s = √(H² + (a/2)²)
Lateral Face Area
A_f = (a × s) / 2
Total Lateral Area
A_l = 4 × A_f = 2 × a × s
Volume
V = (a² × H) / 3
Quick Facts
Great Pyramids of Giza are examples
Base diagonal = a√2
Lateral edge: d = √(H² + a²/2)
Total surface area = A_l + A_b
Understanding Right Square Pyramids
What is a Right Square Pyramid?
A right square pyramid is a three-dimensional geometric shape with a square base and four triangular faces that meet at a single point (apex) directly above the center of the base. The term "right" indicates that the apex is positioned directly over the center of the base, forming a right angle with the base.
Key Components
- •Base Edge (a): Side length of the square base
- •Height (H): Perpendicular distance from base to apex
- •Slant Height (s): Distance from base edge midpoint to apex
- •Lateral Edge (d): Distance from base corner to apex
Area Calculations
Lateral Face Area (A_f)
A_f = (a × s) / 2
Area of one triangular face
Total Lateral Area (A_l)
A_l = 4 × A_f = 2 × a × s
Sum of all four triangular face areas
Total Surface Area (A)
A = A_l + A_b = 2as + a²
Lateral area plus base area
Volume (V)
V = (a² × H) / 3
Base area times height divided by 3