Plane Centroid Calculator
Centroid of composite plane areas from each part's area and centroid. Negative area is a hole. Runs locally. Not a moment of inertia and not a beam calculator.
Trust summary Engine tested · Source checked · 6/6 tests · Production surface contract 6/6 · v1.0.0
- Input interpretation
- Enter values to calculate.
- Result
- —
- Model
- Centroid of a composite plane area from part areas and part centroids.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · 6/6 tests · Production surface contract 6/6 · Source checked · v1.0.0
- Named expert review
- Optional · Not performed
- Sources
- Hibbeler, Engineering Mechanics: Statics
- Evidence
- 2 golden · 4 boundary · Production surface contract 6/6 · Artifact integrity PASS
- Production
- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (3 capabilities; 189 remain CURRENT) @ 2026-09-23T10:40:38.140Z
- Semantic contract
- PASS
Formulas
Core equations used by this calculator.
How to use
Enter each part as A, x, y
One part per row, separated by semicolons. x and y are that part's own centroid.
Use a negative area for a hole
The hole's x and y are the centroid of the removed area.
Read the composite centroid
The result is the first-moment average. Total area must not be zero.
Example calculations
Common configurations with formula and result.
Two equal areas
Area 2 at the origin and area 2 at x = 4
Hole
Area 4 at the origin minus area 2 at x = 3
Plane Centroid calculator specification
Version 1.0.0 · Engine tested
- Engine tested 6/6 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- Plane centroid of signed areas. x̄ = Σ(A x) / ΣA and ȳ = Σ(A y) / ΣA. x and y are the centroid of each part.
- What it calculates
- Centroid of a composite plane area from part areas and part centroids.
- Inputs
- parts
- Outputs
- area
- x_bar
- y_bar
- Formula
x̄ = Σ(A x) / ΣA, ȳ = Σ(A y) / ΣA- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- A negative area removes a hole. This page is not a moment of inertia and not beam deflection.
- Units
- Area and position stay in one consistent unit system. A negative area is a hole.
- Boundary conditions
- no parts → MISSING_REQUIRED_INPUT
- a row that is not A,x,y → INVALID_INPUT
- total area zero → INVALID_INPUT
- Example
- 2,0,0; 2,4,0 → x̄ = 2
- Validation cases
3 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence
- parts=2,0,0; 2,4,0 → area=4, x_bar=2, y_bar=0
- parts=4,0,0; -2,3,0 → area=2, x_bar=-3
- parts=1,0,0; -1,2,0 → INVALID_INPUT
- Sources
- Hibbeler, Engineering Mechanics: Statics — Center of gravity and centroidSupports: x̄ = Σ(A x)/ΣA and ȳ = Σ(A y)/ΣA for a composite plane area
- Hibbeler, Engineering Mechanics: Statics — Center of gravity and centroid
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the centroid of a composite plane area from each part's area and centroid.
Supported and not supported
Supported: signed plane areas, including a hole entered as a negative area.
Not supported: moment of inertia, radius of gyration, section modulus, beam deflection, and mass properties. /calc/mechanical is not open.
Related tools
Other calculators in this family: Planar equilibrium, Area moment, Vector .
Frequently asked questions
Key distinctions behind the calculation.
Does this compute a moment of inertia?
No. It returns the centroid of signed plane areas. Area moments of inertia, radius of gyration, and section modulus are out of scope.
Where does the sum run?
Locally. The first-moment vector calls the vector engine. This page does not contain a second adder.