Prism Calculator
Calculate prism volume and surface area for rectangular, triangular, and hexagonal prisms. Enter dimensions to get total surface area, lateral surface area, and space diagonal.
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Volume
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Total Surface Area —
Lateral Surface Area —
Extended More scenarios, charts & detailed breakdown ▾
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Volume
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Total Surface Area —
Space Diagonal —
Professional Full parameters & maximum detail ▾
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Physical Properties
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Material Planning
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How to Use This Calculator
- Select the Prism Type (Rectangular or Triangular) in the Simple calculator.
- Enter the required dimensions for your chosen shape.
- Use the dedicated tabs for Rectangular, Triangular, or Hexagonal prisms.
- The Professional tab adds weight from density, cross-section area, and material needed with waste percentage.
Formula
Rectangular: V = L×W×H, SA = 2(LW+LH+WH)
Triangular: V = ½×b×h×L, SA = 2×(tri area) + perimeter×L
Example
Rectangular 5×4×3 → V = 60 units³, SA = 94 units². Space diagonal ≈ 7.07 units.
Frequently Asked Questions
- The volume of a rectangular prism (a box) is V = L × W × H, where L is length, W is width, and H is height. For a 5×4×3 box: V = 5 × 4 × 3 = 60 cubic units. Volume is always measured in cubic units (cm³, m³, ft³). If you double all three dimensions, the volume increases by a factor of 2³ = 8. This formula applies to any right prism with a rectangular cross-section — also called a cuboid or rectangular parallelepiped.
- The surface area of a rectangular prism is the total area of all 6 faces. Opposite faces are equal, so: SA = 2(LW + LH + WH). For a 5×4×3 prism: SA = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2 × 47 = 94 square units. Think of it as unfolding the box flat (a "net"): you get two of each pair of faces. Surface area is used to calculate material needed to cover or wrap the prism.
- The volume of a triangular prism equals the area of the triangular cross-section times the length (depth) of the prism: V = (½ × b × h) × L, where b and h are the base and height of the triangle, and L is the prism length. For a triangular cross-section with base 4 and height 3, and prism length 10: V = ½ × 4 × 3 × 10 = 60 cubic units. The triangular cross-section area can also be found using Heron's formula if you know three sides instead of base and height.
- The lateral surface area (LSA) of a prism is the total area of all rectangular side faces, excluding the top and bottom bases. For a rectangular prism: LSA = 2H(L + W), which is the perimeter of the base times the height. For 5×4×3 (H=3): LSA = 2 × 3 × (5 + 4) = 6 × 9 = 54 square units. Total SA = LSA + 2 × base area = 54 + 2 × 20 = 94 sq units (matches). LSA is used when only the sides need to be covered, such as wrapping the sides of a box without top and bottom.
- The space diagonal is the longest distance inside a rectangular box, stretching from one corner to the opposite corner through the interior: d = √(L² + W² + H²). For a 5×4×3 box: d = √(25 + 16 + 9) = √50 ≈ 7.071 units. This is derived by applying the Pythagorean theorem twice: first find the face diagonal f = √(L²+W²), then the space diagonal d = √(f²+H²) = √(L²+W²+H²). The space diagonal equals the diameter of the smallest sphere that can contain the box.