Pivot Tableau Calculator

Pivot Tableau Calculator Form

Enter total rows and columns, then paste the tableau. Use commas or spaces between numbers.

Number of Rows

Number of Columns

Decimal Places

Pivot Row

Pivot Column

Column Labels

Row Labels

Tableau Values

Example row format: 2, 1, 1, 0, 18

Example Data Table

This sample represents a simple simplex tableau with two constraints and one objective row.

Row	x1	x2	s1	s2	RHS
R1	2	1	1	0	18
R2	2	3	0	1	42
Z	-3	-2	0	0	0

Rows: 3
Columns: 5
Pivot row: 2
Pivot column: 2

Formula Used

A pivot tableau update applies elementary row operations to convert one pivot column entry into a unit basis entry.

1) Pivot element

The pivot element is the number located at the chosen pivot row and pivot column.

Pivot element: a_{pr, pc}

2) Normalize the pivot row

Divide every value in the pivot row by the pivot element.

New pivot row: R_p = R_p / a_{pr, pc}

3) Eliminate the other pivot-column entries

For each non-pivot row, subtract its pivot-column entry multiplied by the new pivot row.

New row i: R_i = R_i - a_{i, pc} × R_p

4) Optional ratio test

When simplex work requires a leaving row, the usual check divides the RHS by each positive pivot-column entry.

Ratio: RHS / pivot-column entry

How to Use This Calculator

Enter the full tableau size, including the RHS column.
Provide the pivot row and pivot column using 1-based positions.
Paste tableau values row by row into the textarea.
Add custom row and column labels if needed.
Click Calculate Pivot to transform the tableau.
Review the original and transformed tables above the form.
Inspect the row-operation steps and ratio checks.
Download the transformed tableau as CSV or PDF.

FAQs

1) What does this calculator do?

It performs one pivot operation on a simplex tableau. The tool normalizes the pivot row, removes other entries in the pivot column, shows the updated tableau, and lists each row operation clearly.

2) What is a pivot element?

The pivot element sits at the chosen pivot row and pivot column. It must be nonzero. That value is used to scale the pivot row and eliminate every other entry in the same column.

3) Why is the RHS usually the last column?

In simplex tableaus, the final column commonly stores the right-hand-side constants. Keeping RHS last makes ratio checks easier and keeps the tableau structure consistent across iterations.

4) Can I enter decimals or negative values?

Yes. The calculator accepts integers, decimals, and negative values. Separate entries with commas, spaces, or semicolons. Each row must still contain the exact number of values required by the column setting.

5) What happens if the pivot element is zero?

A zero pivot element cannot normalize the pivot row. The calculator stops and shows an error. Choose a different pivot position or correct the input tableau before calculating again.

6) Does the ratio table automatically choose the pivot row?

No. You choose the pivot row manually. The ratio table is still useful because it shows positive RHS-to-entry ratios, which often support leaving-row decisions during simplex iterations.

7) What does the graph show?

The graph compares the selected pivot-column values before and after the pivot step. This helps you verify that the pivot row becomes one and the other pivot-column entries move toward zero.

8) Can I use this for learning simplex manually?

Yes. The calculator is useful for study and checking hand calculations. It shows the original tableau, transformed tableau, row operations, ratio checks, and exportable outputs for review.