Math / CALCULATOR

Point-Mass Center Calculator

Point-Mass Center Calculator: explicit measurements, a worked example and input validation.

Runs on your deviceUpdates as you typeFormula & example ↓
01

Your inputs

Adjust the values to explore a different result.

One positive mass and two coordinates per row; 1–100 rows.

Formula

x̄=Σmᵢxᵢ/Σmᵢ; ȳ=Σmᵢyᵢ/Σmᵢ.
  • Use the units shown beside each field.
  • Results update automatically whenever you change an input.
  • Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
  • Discrete point masses in two dimensions; not a continuous density integral. Mass units must agree.

Example Calculation

Example inputs
  • Rows: mass, x, y: 1, 0, 0; 3, 4, 0

Masses 1 at (0,0) and 3 at (4,0) give center (3,0) and total mass 4.

Frequently asked questions

How do I use this calculator?

Enter rows: mass, x, y. The result updates automatically. Use Reset to restore the example values.

What method does it use?

x̄=Σmᵢxᵢ/Σmᵢ; ȳ=Σmᵢyᵢ/Σmᵢ.. Discrete point masses in two dimensions; not a continuous density integral. Mass units must agree.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.