How to Calculate the Surface Area of a Rectangular Prism

by

Rectangular Prism Surface Area Calculator

Calculate the total external area of any box-shaped object

Result:

Understanding the Surface Area of a Rectangular Prism

A rectangular prism (also known as a rectangular cuboid) is a three-dimensional solid shape which has six faces that are all rectangles. Calculating the surface area is essential for tasks like wrapping a gift, painting a room, or determining the amount of material needed to manufacture a shipping box.

The Formula

The total surface area is the sum of the areas of all six faces. Since opposite faces are identical, we calculate three pairs of areas and add them together:

Surface Area = 2lw + 2lh + 2wh
  • l = Length of the prism
  • w = Width of the prism
  • h = Height of the prism

How to Calculate Step-by-Step

  1. Identify the Dimensions: Find the length, width, and height of your object.
  2. Calculate Top/Bottom: Multiply length by width (lw) and then multiply by 2.
  3. Calculate Front/Back: Multiply length by height (lh) and then multiply by 2.
  4. Calculate Sides: Multiply width by height (wh) and then multiply by 2.
  5. Sum the Totals: Add those three results together to get the total surface area in square units.

Practical Example

Imagine you have a box that is 10 inches long, 5 inches wide, and 4 inches high.

  • Step 1: Area of Top/Bottom = 10 × 5 = 50 sq in (x2 = 100)
  • Step 2: Area of Front/Back = 10 × 4 = 40 sq in (x2 = 80)
  • Step 3: Area of Sides = 5 × 4 = 20 sq in (x2 = 40)
  • Total Surface Area: 100 + 80 + 40 = 220 square inches
function calculateSurfaceArea() { var l = parseFloat(document.getElementById('prismLength').value); var w = parseFloat(document.getElementById('prismWidth').value); var h = parseFloat(document.getElementById('prismHeight').value); var resultArea = document.getElementById('resultArea'); var finalOutput = document.getElementById('finalOutput'); var calculationBreakdown = document.getElementById('calculationBreakdown'); if (isNaN(l) || isNaN(w) || isNaN(h) || l <= 0 || w <= 0 || h <= 0) { alert("Please enter valid positive numbers for all dimensions."); resultArea.style.display = 'none'; return; } // Formulas var topBottom = l * w; var frontBack = l * h; var sides = w * h; var totalArea = 2 * (topBottom + frontBack + sides); // Displaying Results finalOutput.innerText = totalArea.toLocaleString() + " Square Units"; calculationBreakdown.innerHTML = "Calculation breakdown:" + "2 × (" + l + " × " + w + ") + 2 × (" + l + " × " + h + ") + 2 × (" + w + " × " + h + ") = " + totalArea + "" + "• Top & Bottom: " + (2 * topBottom) + " units²" + "• Front & Back: " + (2 * frontBack) + " units²" + "• Left & Right Sides: " + (2 * sides) + " units²"; resultArea.style.display = 'block'; // Smooth scroll to result resultArea.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }

Leave a Comment