Calculators
Rectangular Pyramid Frustum Calculator
Calculate right rectangular pyramid frustum volume, derived top width, slant heights, and lateral and total surface areas.
Measure a frustum with similar rectangular bases.
A right rectangular pyramid frustum has similar rectangular bases in parallel planes, centered on one perpendicular axis with corresponding edges aligned. Enter bottom length L, bottom width W, top length l, and perpendicular height h. Use the larger base as the bottom, with 0 < l ≤ L. The top width is w = Wl/L; independent top dimensions would not necessarily form a pyramid frustum. With k = l/L, bottom area B = LW and top area b = lw, volume V = Bh(1 + k + k²)/3. The slant height of the faces along the length edges is sₗ = √(h² + ((W − w)/2)²); along the width edges it is sᵥ = √(h² + ((L − l)/2)²). Lateral area A = (L + l)sₗ + (W + w)sᵥ. Total closed surface area is A + B + b. For L = 8, W = 6, l = 4, and h = 3, top width is 3, volume is 84 cubic units, and lateral area is approximately 72.6991850742 square units. Equal top and bottom lengths give a rectangular prism. These formulas exclude oblique, twisted, or independently proportioned bases. Use one consistent length unit from 1e-50 to 1e50; derived dimensions may be smaller. Scientific notation is accepted. Results use browser floating-point arithmetic rounded to 12 significant digits. This solid model does not account for wall thickness or hollow capacity. All inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Why is top width calculated automatically?
A pyramid frustum requires similar bases. Both top dimensions must use the same scale factor, so top width equals bottom width multiplied by top length divided by bottom length. Arbitrary top dimensions describe a different solid.
What does the surface area include?
Lateral area includes the four trapezoidal faces. Total closed surface area also includes both rectangular bases. The two pairs of faces generally have different slant heights.
Can I use equal bases?
Yes. Equal top and bottom lengths produce a right rectangular prism. Top length must be positive and cannot exceed bottom length. Use the larger base as the bottom.
Which units and shapes are supported?
Use consistent length units from 1e-50 to 1e50, including scientific notation. Height is perpendicular to the bases. The bases must be similar, aligned and centered; oblique or twisted frustums are excluded. Computation stays in your browser.