Calculator Servicescalculatorservices.com
Mathematics

Weighted Average (3 values)

Σ(wᵢ xᵢ) / Σwᵢ. Free online Weighted Average (3 values). Calculate weighted average (3 values) online — fast, accurate, mobile-friendly, no signup needed.

Weighted average
84.5

Derivation

  1. ├── 01Givenx1 = 80, w1 = 0.3, x2 = 85, w2 = 0.5, x3 = 90, w3 = 0.2
  2. ├── 02Formula{let t=e.x1,a=e.w1,n=e.x2,r=e.w2,o=e.x3,l=e.w3;return(t × a+n × r+o × l) / (a+r+l)}
  3. ├── 03Substitute{let t=e.80,a=e.0.3,n=e.85,r=e.0.5,o=e.90,l=e.0.2;return(t × a+n × r+o × l) / (a+r+l)}
  4. └── 04Compute Weighted average84.5
Did you know?

Every calculator here runs 100% in your browser — nothing is sent to a server or stored in a database.

§01What is

Understanding the Weighted Average (3 values)

The Weighted Average (3 values) computes Weighted average from 6 inputs: x₁, w₁, x₂, w₂, x₃, w₃. Σ(wᵢ xᵢ) / Σwᵢ.

Mathematics shows up in every corner of daily life — budgeting, cooking, construction, engineering, even reading a bus schedule. A calculator like this lets you skip the scratch-paper step and move straight to the answer, without the arithmetic mistakes that creep in when the numbers get messy. The Weighted Average (3 values) sits in that toolkit — it Σ(wᵢ xᵢ) / Σwᵢ. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

{let t=e.x1,a=e.w1,n=e.x2,r=e.w2,o=e.x3,l=e.w3;return(t × a+n × r+o × l) / (a+r+l)}

Where

x1
x₁
w1
w₁
x2
x₂
w2
w₂
x3
x₃
w3
w₃
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: x₁ = 80, w₁ = 0.3, x₂ = 85, w₂ = 0.5, x₃ = 90, w₃ = 0.2.

  1. 01Start by noting the input — x₁: 80.
  2. 02Start by noting the input — w₁: 0.3.
  3. 03Start by noting the input — x₂: 85.
  4. 04Start by noting the input — w₂: 0.5.
  5. 05Start by noting the input — x₃: 90.
  6. 06Start by noting the input — w₃: 0.2.
  7. 07Substitute these values into the formula: {let t=e.x1,a=e.w1,n=e.x2,r=e.w2,o=e.x3,l=e.w3;return(t × a+n × r+o × l) / (a+r+l)}
  8. 08Compute Weighted average: the calculator returns 84.5.
  9. 09Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Weighted Average (3 values) Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

x₁ halved

x1 = 40 (from 80)

Keep every other input at its default and halve the x₁. See how weighted average responds.

  1. 01New x₁: 40
  2. 02Baseline Weighted average: 84.5
  3. 03New Weighted average: 72.5
  4. 04Weighted average decreases by 14.2% → use this sensitivity to plan for real-world variation.
02 · PATTERN

x₁ doubled

x1 = 160 (from 80)

Keep every other input at its default and double the x₁. See how weighted average responds.

  1. 01New x₁: 160
  2. 02Baseline Weighted average: 84.5
  3. 03New Weighted average: 108.5
  4. 04Weighted average increases by 28.4% → use this sensitivity to plan for real-world variation.
03 · PATTERN

w₁ halved

w1 = 0.15 (from 0.3)

Keep every other input at its default and halve the w₁. See how weighted average responds.

  1. 01New w₁: 0.15
  2. 02Baseline Weighted average: 84.5
  3. 03New Weighted average: 85.2941
  4. 04Weighted average increases by 0.9% → use this sensitivity to plan for real-world variation.
04 · PATTERN

w₁ doubled

w1 = 0.6 (from 0.3)

Keep every other input at its default and double the w₁. See how weighted average responds.

  1. 01New w₁: 0.6
  2. 02Baseline Weighted average: 84.5
  3. 03New Weighted average: 83.4615
  4. 04Weighted average decreases by 1.2% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
Your feedback

How useful was this calculator?

Your ratings stay in your browser — they help us learn which tools people actually rely on.

Rate it
Was this helpful?