Triangle Centroid
The centroid is simply the average of the three coordinates. It is where the medians meet, and a paper triangle balances on it. The area comes from the shoelace formula.
Your numbers
Centroid x
3.667
Centroid y
3
Area
25
Formula
Centroid x = (x₁ + x₂ + x₃) ÷ 3
The centroid cuts each median in a 2:1 ratio — two parts towards the vertex, one towards the opposite side.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| x₁The horizontal coordinate of the first point. | 0 | No limit |
| y₁The vertical coordinate of the first point. | 0 | No limit |
| x₂The horizontal coordinate of the second point. | 8 | No limit |
| y₂The vertical coordinate of the second point. | 2 | No limit |
| x₃The horizontal coordinate of the third point. | 3 | No limit |
| y₃The vertical coordinate of the third point. | 7 | No limit |
Step by step
Quick reference table
Results when only x₂ changes and everything else stays put.
| x₂ | Centroid x | Centroid y | Area |
|---|---|---|---|
| 4 | 2.333 | 3 | 11 |
| 6 | 3 | 3 | 18 |
| 8 | 3.667 | 3 | 25 |
| 12 | 5 | 3 | 39 |
| 16 | 6.333 | 3 | 53 |
What each result means
| Result | At default values |
|---|---|
| Centroid xThe average of the three x values — the centroid’s x. | 3.667 |
| Centroid yThe average of the three y values — the centroid’s y. | 3 |
| AreaThe space a shape covers — length squared. | 25 |
Common mistakes
The centroid cuts each median in a 2:1 ratio — two parts towards the vertex, one towards the opposite side.
Glossary
- x₁
- The horizontal coordinate of the first point.
- y₁
- The vertical coordinate of the first point.
- x₂
- The horizontal coordinate of the second point.
- y₂
- The vertical coordinate of the second point.
- x₃
- The horizontal coordinate of the third point.
- y₃
- The vertical coordinate of the third point.
- Centroid x
- The average of the three x values — the centroid’s x.
- Centroid y
- The average of the three y values — the centroid’s y.
- Area
- The space a shape covers — length squared.
Frequently asked questions
Q. How is Triangle Centroid calculated?
Centroid x = (x₁ + x₂ + x₃) ÷ 3 — The centroid is simply the average of the three coordinates. It is where the medians meet, and a paper triangle balances on it. The area comes from the shoelace formula.
Q. Can you walk through an example?
With x₁ 0, y₁ 0, x₂ 8, y₂ 2, x₃ 3, y₃ 7, the answer is Centroid x 3.667.
Q. What do I need to enter?
Enter x₁, y₁, x₂, y₂, x₃, y₃. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only x₂ moves the answer to x₂ 4 → Centroid x 2.333 and x₂ 16 → Centroid x 6.333. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
The centroid cuts each median in a 2:1 ratio — two parts towards the vertex, one towards the opposite side.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.