Calculator Inputs
Use decimal mode for direct factors like 0.97. Use percent mode for entries like 97.
Example Data Table
| η | f | p | ε | PFNL | PTNL | k∞ | keff | State |
|---|---|---|---|---|---|---|---|---|
| 2.05 | 0.74 | 0.87 | 1.03 | 0.97 | 0.96 | 1.355153 | 1.261623 | Supercritical |
| 1.88 | 0.69 | 0.82 | 1.01 | 0.94 | 0.92 | 1.075594 | 0.930901 | Subcritical |
| 2.00 | 0.72 | 0.85 | 1.02 | 0.96 | 0.95 | 1.248480 | 1.138613 | Supercritical |
Formula Used
k∞ = η × f × p × ε
keff = k∞ × PFNL × PTNL
ρ = (keff − 1) / keff
pcm = ρ × 100000
Nn = N0 × keffn
Total = N0 × (1 − keffn+1) / (1 − keff), for keff ≠ 1
A system is subcritical when keff < 1, critical when keff = 1, and supercritical when keff > 1. The calculator also checks whether the uncertainty band crosses 1.0, which is useful for quick screening.
How to Use This Calculator
- Select decimal mode if your factors are already in decimal form.
- Select percent mode if your factors are entered as values like 97 or 74.
- Fill in η, f, p, ε, fast non-leakage, and thermal non-leakage.
- Enter the initial neutron population and number of generations if growth estimation is needed.
- Set the target k value, usually 1.0 for critical operation checks.
- Add an uncertainty percentage to see a practical confidence band.
- Press Calculate Factor to show results above the form.
- Use the export buttons to save the current result as CSV or PDF.
FAQs
1) What does the multiplication factor represent?
It measures whether each neutron generation produces fewer, equal, or more neutrons than the previous generation. It is central to judging reactor criticality and system stability.
2) Why are there both k∞ and keff values?
k∞ assumes no neutron leakage from the system. keff includes leakage losses, so it better reflects real finite systems and practical reactor behavior.
3) What do η, f, p, and ε mean?
These are the standard four factors: reproduction factor, thermal utilization factor, resonance escape probability, and fast fission factor. Together they define multiplication before leakage losses.
4) What does reactivity tell me?
Reactivity expresses how far the system is from exact criticality. Positive values indicate supercritical behavior, zero indicates criticality, and negative values indicate subcritical behavior.
5) Why include an uncertainty percentage?
Measurements and models are never perfect. The uncertainty band shows whether the result stays clearly above or below 1.0, or whether the system may lie close to critical.
6) Can this calculator predict actual reactor safety?
No. It is a simplified educational and analytical tool. Real reactor analysis requires detailed neutronics, thermal-hydraulics, material data, operating conditions, and regulated safety methods.
7) What happens when keff equals 1?
The neutron population remains steady from one generation to the next. This is the idealized critical condition for a stable chain reaction.
8) Why estimate neutron population over generations?
It helps visualize how small changes in keff influence growth or decay over time. Even slight deviations from 1.0 can strongly affect neutron population trends.