About

An addition table maps the sum a + b for every pair within a chosen range. Errors in basic arithmetic propagate through every downstream calculation - budgeting, engineering tolerances, dosage tables - so a verified reference grid eliminates that risk at the source. This generator builds tables up to 30 × 30 (900 cells), applies an optional heat-map to expose magnitude patterns, and outputs a print-ready sheet that fits A4 paper. The tool assumes integer addends only; fractional or negative arithmetic is outside scope.

Formulas

Each cell in the addition table is computed by the identity:

S_i,j = i + j

where S_i,j is the cell value at row i and column j, and both i and j range from the user-defined minimum a to maximum b.

The total number of cells generated is:

N = (b − a + 1)²

The mean value across all cells is:

S = a + b

The optional heat-map normalizes each cell value to a 0 - 1 scale using:

t = S_i,j − 2a2b − 2a

where t is then mapped to an HSL hue from 200° (cool blue) to 0° (warm red).

Reference Data

Range	Cells	Min Sum	Max Sum	Mean Sum	Use Case
1 - 5	25	2	10	6.0	Pre-school introduction
1 - 10	100	2	20	11.0	Primary school drill
1 - 12	144	2	24	13.0	Standard classroom chart
1 - 15	225	2	30	16.0	Extended practice
1 - 20	400	2	40	21.0	Mental math training
1 - 25	625	2	50	26.0	Speed arithmetic
1 - 30	900	2	60	31.0	Advanced reference
0 - 10	121	0	20	10.0	Identity element study
0 - 20	441	0	40	20.0	Full beginner set with zero
5 - 15	121	10	30	20.0	Mid-range focus drill
10 - 20	121	20	40	30.0	Two-digit sum practice
15 - 30	256	30	60	45.0	Advanced two-digit sums

Frequently Asked Questions

Addition is commutative: a + b = b + a. This means cell (i, j) always equals cell (j, i), producing mirror symmetry along the main diagonal. You can use the highlight feature to click any cell and visually confirm its symmetric partner.

Each cell value is normalized to a 0-1 range between the minimum possible sum (2a) and maximum possible sum (2b). This normalized value is mapped to an HSL hue: 200° (blue) for the smallest sums, transitioning through green to 0° (red) for the largest. Saturation is fixed at 65% and lightness at 85% to maintain pastel readability.

The maximum range is 0 to 30, producing up to 961 cells (31 × 31). DOM generation for this count completes in under 50ms on modern hardware. No Web Workers are needed. The practical bottleneck is print layout - tables beyond 20 columns may require landscape orientation or reduced font size for A4 paper.

Yes. Setting the minimum to 0 includes the additive identity element. The row and column for 0 will simply mirror the header values since n + 0 = n. This is pedagogically useful for teaching the identity property of addition.

Each anti-diagonal (running from upper-right to lower-left) contains cells with the same sum. For example, in a 1-10 table, every cell on the anti-diagonal where i + j = 7 holds the value 7. The highlight-row-column feature helps visualize this. The number of cells on each anti-diagonal follows a triangular distribution, peaking at the middle sum value.

Yes, provided your browser's print dialog has "Background graphics" enabled (this is off by default in most browsers). The print stylesheet adjusts font sizes and hides interactive controls, but retains cell background colors. For black-and-white printers, disable the heat-map option before printing to get a clean numeric grid.