Weighted Average Calculator

Unlike a standard arithmetic mean that treats every data point equally, a weighted average assigns a specific coefficient or weight to each value based on its significance. The mathematical formula is expressed as:

Weighted Average = Σ(x_i × w_i) / Σ(w_i)

Where x_i represents each individual value and w_i represents its corresponding weight. You multiply each value by its weight, sum all of those products together, and then divide that cumulative sum by the total sum of all the weights combined.

Imagine you want to calculate your final grade for a course where assignments carry different weights:

• Homework: Grade of 85, weighted at 20% (weight = 0.20)
• Midterm Exam: Grade of 78, weighted at 30% (weight = 0.30)
• Final Project: Grade of 92, weighted at 50% (weight = 0.50)

Step 1: Multiply each score by its weight.

• 85 × 0.20 = 17.0
• 78 × 0.30 = 23.4
• 92 × 0.50 = 46.0

Step 2: Add these products together to find the numerator: 17.0 + 23.4 + 46.0 = 86.4.

Step 3: Sum the weights: 0.20 + 0.30 + 0.50 = 1.00.

Step 4: Divide the numerator by the total weight sum: 86.4 / 1.00 = 86.4. Your final weighted grade is 86.4%.

Always verify whether your weights add up to 100% (or 1.0 if using decimals). If your weights sum to a different number, make sure you divide by the actual sum of the weights rather than assuming a base of 100. Additionally, keep your input units consistent across all entries to prevent skewed calculations.