Masspoint field notes
A point for the whole layout
Start with a small arrangement you can describe on paper: several items, a mass for each item, and a position for each item's mass centre. Masspoint combines those entries into one planar centre. The useful part is the record of what went into the answer. You can inspect every row, retain exact fractions, and compare a changed arrangement without losing your starting coordinate system.
Choose the origin before measuring
Pick a reference that you can identify again, such as the left corner of a tabletop drawing. Call that reference (0, 0). Decide which direction is positive x and which is positive y. Measure the centre position of every item from that same reference. A position to the left can have a negative x value; a position below the chosen horizontal axis can have a negative y value. A negative coordinate describes location, not negative mass.
For objects arranged along a straight line, use the distance along the line as x and put 0 in every y field. You do not need a separate mode. For a flat arrangement, enter both coordinates. The picture preserves the shape of the entered point layout but does not show the outlines or dimensions of the actual objects. Numbered markers connect the picture with the input rows.
The calculation, with names kept explicit
Masspoint adds the positive masses to get M. It separately adds mass multiplied by x, and mass multiplied by y. Dividing each weighted sum by M gives the two centre coordinates. These are the point-mass component equations described in OpenStax University Physics, section 9.6.
x centre = Σ(m × x) / M
y centre = Σ(m × y) / M
The displayed weighted sums are labelled Σ m·x and Σ m·y. This avoids mixing up axis names: a conventional moment about the y-axis uses x, while a moment about the x-axis uses y. The OpenStax moments reference explains that naming convention. The tool does not calculate torque from applied forces.
Example: three pieces on a small mock-up
Enter 100 g at (0, 0) mm, 200 g at (300, 0) mm, and 100 g at (0, 240) mm. The total is 400 g. The x weighted sum is 100×0 + 200×300 + 100×0 = 60,000 g·mm. The y weighted sum is 100×0 + 200×0 + 100×240 = 24,000 g·mm.
Dividing by 400 gives x = 150 mm and y = 60 mm. The heavier right-hand piece pulls the combined point toward its position. If you change only its mass from 200 g to 400 g, the new total is 600 g and the centre becomes (200, 40) mm. No coordinate changed; the weighting changed.
Keep both reports if you are comparing versions of the mock-up. The CSV contains the input rows and a separate centre record, so it remains clear which arrangement produced each result. File names are generic; rename the downloaded files if you need to distinguish versions.
Example: signed positions that cancel
Try 40 g at (−120, 30) mm and 60 g at (80, −20) mm. The x products are −4,800 and +4,800 g·mm. The y products are +1,200 and −1,200 g·mm. Both weighted sums are zero, so the combined centre is exactly (0, 0). Neither item has zero mass, and neither item is at the origin. Cancellation is a result of their signed positions and different masses.
Now move your coordinate origin. If every entered x is reduced by 50 mm and every entered y increased by 25 mm, the resulting centre becomes (−50, 25) mm. The physical arrangement is the same; its coordinate description changed. This is a useful check when two drawings use different references.
Example: a fraction that should stay a fraction
Enter 2 g at (0, 0) mm and 1 g at (1, 1) mm. The answer is (1/3, 1/3) mm. A short decimal cannot express that exactly. The summary gives an approximate decimal when needed, and the expanded exact-results section and reports retain 1/3. Typing 0.333333 instead would describe a slightly different input.
Fractions use an integer numerator and a positive integer denominator, such as −5/8. A denominator of zero is rejected. Mixed numbers such as “1 1/2” are not accepted; enter 3/2 or 1.5. Scientific notation and thousands separators are also rejected so that commas keep their single role of separating mass, x and y.
Units that preserve the entered arrangement
Use grams, kilograms or avoirdupois pounds for mass, and millimetres, centimetres, metres or international inches for coordinates. Every row shares the selected units. The unit controls convert the entire input rather than merely relabelling it. Exact fractions may appear after a conversion; they preserve an entered value that would otherwise need a rounded repeating decimal.
The inch factor is exactly 25.4 mm, as recorded by NIST's metrology FAQ. The avoirdupois pound is exactly 0.45359237 kg; see NIST SI footnote 22. For a check, use 1 lb at (0, 0) inches and 3 lb at (4, 2) inches. The total is 4 lb and the centre is (3, 1.5) inches. Converting to metric gives 1814.36948 g at (76.2, 38.1) mm.
Extremely long input fractions can produce converted fractions beyond the supported input length. The complete converted input must also stay within the same 12,000-character limit as typed input. If either limit is exceeded, the unit change is refused and the original values, units and valid result stay in place. This is a software-size boundary, not a physical rule. Shorter equivalent input is often easier to review anyway.
What belongs in a row
A row represents a mass placed at its own mass centre. If a component's mass is spread out, use a centre position you have already established for that component. The tool cannot infer it from a corner coordinate. A uniform rectangular board, an uneven assembly and a hollow enclosure may need different ways of locating their own centres before you combine them.
Include supporting pieces if they are part of the system you mean to model. Leaving out a board's mass does not make the board massless in reality; it simply leaves that mass out of this calculation. Likewise, counting a component twice changes the answer. A row number is only a reference, not a quantity multiplier.
Check the model before keeping the answer
Read the row count and total mass first. Confirm the coordinate signs, the origin and the selected units. For positive masses, each centre coordinate must lie between the smallest and largest entered coordinate on that axis. A single row returns that row's position. Equal masses at opposite positions give a centre at their midpoint. These quick checks help catch a transposed value.
The model stays planar: it has no third coordinate, no support polygon, no applied forces and no dynamic motion. A combined mass centre alone does not establish safe suspension, contact pressure, attachment capacity or resistance to tipping. The exact arithmetic does not remove uncertainty in a scale reading or a measured position. Keep the reported precision appropriate to the measurements you actually made.
A report you can inspect later
Text and CSV downloads are created locally from the current valid result. Copying uses the browser clipboard when available and provides a manual text box when permission is denied. Editing or resetting clears an older copy message. Invalid input hides the previous calculation and disables exports, which keeps an earlier answer from looking current. Your inputs are not stored by this calculator, so save a report before leaving if you need it later.