Reactor Criticality Helper
Compute k-eff, reactivity (rho and dollars), and reactor period from neutron generation and loss rates.
Neutron Balance Inputs
Kinetics Parameters (optional)
U-235 thermal: 0.0065 | Pu-239: 0.0021 | U-233: 0.0026
Thermal reactors ~50–100 μs | Fast reactors ~0.1–1 μs
Typical U-235 composite ~13 s
Effective Multiplication Factor
Reactivity ρ
—
Δk/k (dimensionless)
Reactivity pcm
—
1 pcm = 10-5
Reactivity $
—
ρ / β
Reactor Period (Inhour approximation)
Prompt period Tp
—
(prompt neutrons only)
Stable period T (with delayed)
—
(single-group delayed approx.)
Prompt-critical warning
Reactivity exceeds 1 dollar (ρ > β). The reactor is prompt-critical — power rises on prompt neutrons alone. This is the key design safety boundary.
Formulas used
k-eff = Production / (Absorption + Leakage)
ρ = (k-eff − 1) / k-eff
Reactivity $ = ρ / β
Prompt period Tp = ℓ* / ρ (for ρ > 0)
Stable period T = (ℓ* + βℓd) / ρ (single-group, ρ > 0)
Point-kinetics approximation. Educational use only.
Summary
Compute k-eff, reactivity (rho and dollars), and reactor period from neutron generation and loss rates.
How it works
- Enter the neutron production rate and neutron absorption/leakage rate.
- The tool computes k-eff as the ratio of neutrons produced to neutrons lost per generation.
- Reactivity (rho) is derived from k-eff: rho = (k-eff − 1) / k-eff.
- Enter the delayed neutron fraction (beta) to convert reactivity from rho to dollars.
- Enter the prompt neutron lifetime to compute the prompt and delayed reactor period.
Use cases
- Verify reactor criticality conditions in academic nuclear engineering courses.
- Estimate reactivity worth of control rod movements in simplified models.
- Convert reactivity units between rho (delta-k/k) and dollars during design review.
- Compute reactor period to estimate power doubling time during startup.
- Cross-check hand calculations for criticality safety assessments.
- Demonstrate neutron balance concepts in training exercises.