Iterative Calculation Calculator
Example Data Table
| Example | Start | Target/Base | Rate | Formula Pattern | Use Case |
|---|---|---|---|---|---|
| Goal seek | 10 | 100 | Not needed | Previous plus damped gap | Move toward a known answer |
| Growth | 500 | Not needed | 5% | Previous times growth plus addition | Repeated increase model |
| Newton root | 8 | 64 | Not needed | Average of guess and quotient | Square root approximation |
| Circular fee | 100 | 1000 | 8% | Base plus fee on previous gross | Gross-up or circular charge |
Formula Used
The calculator uses one rule at a time. The goal seek rule is: Next = Previous + Damping × (Target - Previous).
The growth rule is: Next = Previous × (1 + Rate ÷ 100) + Fixed Addition.
The Newton rule is: Next = (Previous + Target ÷ Previous) ÷ 2. Here, target means the number whose square root is being estimated.
The circular fee rule is: Next = Base + Previous × (Rate ÷ 100) + Fixed Addition. This imitates a circular sheet reference.
How To Use This Calculator
- Select the iterative example type.
- Enter the initial guess and target or base value.
- Add the percent rate, fixed addition, and damping value if needed.
- Set tolerance and maximum iterations.
- Choose the stop rule.
- Press Calculate.
- Review the result and row history.
- Download the CSV or PDF report if required.
Practical Iteration For Sheet Models
Iterative calculation is useful when one answer depends on a previous answer. Many sheet users meet it while testing circular references, goal seeking, growth paths, or repeated estimates. A normal formula solves once. An iterative model solves again and again until the change becomes small enough.
This calculator mirrors that workflow. It starts with an initial guess. It applies the selected rule. Then it compares the new value with either the target, the previous value, or both. The loop stops when the tolerance is reached. It also stops when the iteration limit is reached.
Google Sheets can handle iterative calculation after the setting is enabled. The setting helps circular formulas work without showing an immediate error. Yet the result still depends on three choices. The starting value matters. The maximum number of iterations matters. The convergence threshold matters too.
Use the goal approach when a value should move toward a known target. It is helpful for budgets, percentages, and planned balances. Use the growth option when a value changes by a fixed rate and addition. This can model compounding, recurring fees, or stock estimates. Use the Newton option when explaining square root approximation. Use the circular fee option when a gross amount depends on its own fee.
The tolerance field controls accuracy. A smaller tolerance means a stricter stop rule. It may need more steps. A larger tolerance gives a faster answer. It may be less precise. The damping field controls how strongly each step moves. Lower damping can calm unstable models. Higher damping can make convergence faster.
The exported CSV is useful for checking every step. The PDF gives a compact report for sharing. The example table shows how each row can represent one sheet row. This makes the tool helpful for tutorials, audits, and classroom examples.
Always review the row history. A converged result should show smaller errors over time. If errors grow, change the method, damping, or start value. Iterative models are powerful. They are also sensitive. Clear inputs make them easier to trust.
For best results, keep units consistent. Name each sheet row clearly. Save a copy before testing circular formulas in important workbooks. Document assumptions beside the output for review.
FAQs
What is iterative calculation?
Iterative calculation repeats a formula until a stopping rule is met. It is often used when a result depends on its own earlier value.
Why does the initial guess matter?
The first value can affect the path and speed of convergence. Some models may fail when the starting value is too far away.
What does tolerance mean?
Tolerance is the allowed difference before the loop stops. Smaller tolerance gives stricter results, but it may require more iterations.
What is damping?
Damping reduces the size of each move toward the target. It can help unstable iterative models settle more smoothly.
Which example matches circular references?
The circular fee option is closest. It estimates a gross amount when the fee depends on the gross amount itself.
Can this replace a spreadsheet model?
It helps test logic and explain steps. You should still verify final business models inside the actual workbook.
Why did my result not converge?
The method, rate, guess, or damping may be unsuitable. Try fewer aggressive settings, a better initial value, or a different example type.
What does the CSV export include?
The CSV includes summary values and iteration rows. It is useful for checking each repeated step in a spreadsheet.