Nuclear Reactor Period Calculator
Calculates the reactor period, the time for power to change by a factor of e, from a measured power change or from reactivity with one delayed neutron group.
Last updated: October 2026
Reactor Period
86.56 seconds
Formula below · 3 sources (ansn.iaea.org, cedengineering.com, et.byu.edu) · Updated Oct 2026
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About this calculator
The reactor period T is the time for reactor power to change by a factor of e (about 2.718): P(t) = P₀ × e^(t/T). A positive period means power is rising, a negative one that it is falling.
From a measured power change
If power goes from P₁ to P₂ in a time Δt, T = Δt ÷ ln(P₂/P₁). This uses only the definition, so it holds for any reactor.
From reactivity
For a reactivity step ρ below prompt critical, the one-delayed-group approximation gives T ≈ ℓ/ρ + (β − ρ)/(λρ), where ℓ is the prompt neutron lifetime, β = 0.0065 is the delayed neutron fraction of U-235 and λ is an effective decay constant of the delayed neutron precursors, about 0.08 s⁻¹ (the calculator uses 0.0767 s⁻¹, the value that matches the six-group U-235 data on average). Because ℓ is tiny, the delayed neutrons set the period: ρ = 0.001 gives about 72 s.
Limits
At ρ ≥ β the reactor is prompt critical and the period drops to fractions of a second; the formula no longer applies. After a large negative reactivity insertion, such as a scram, power cannot fall faster than the longest-lived precursor group allows, which gives a period of about −80 s; the calculator does not report negative periods shorter than that.
How to use
Example 1, measured (default): power rises from 100 MW to 200 MW in 60 s. T = 60 ÷ ln 2 = 86.56 s. From 100 to 150 MW in 30 s: T = 30 ÷ ln 1.5 = 73.99 s. A fall from 100 to 50 MW in 120 s gives −173.12 s. Example 2, from reactivity: ρ = 0.001 Δk/k and ℓ = 1×10⁻⁵ s, Method = From reactivity. T = 10⁻⁵ ÷ 0.001 + (0.0065 − 0.001) ÷ (0.0767 × 0.001) = 0.01 + 71.71 = 71.72 s. With ρ = 0.002 the period shortens to 29.34 s.
Frequently asked questions
What is the reactor period and why does it matter?
It is the time constant of exponential power change: the time for power to grow (or shrink) by a factor of e. Operators watch it during start-up because a short positive period means power is climbing fast, and protection systems act on short periods.
Why do delayed neutrons make the period so much longer?
A small fraction of fission neutrons (β ≈ 0.65% for U-235) are emitted seconds to about a minute later by decaying fission products. Below prompt critical, the chain reaction has to wait for them, which stretches the period from milliseconds to tens of seconds.
Why is the negative period capped at −80 seconds?
After a scram, power falls only as fast as the longest-lived delayed neutron precursors decay, which gives a stable negative period of about −80 s whatever the size of the negative reactivity.
Is the one-group result exact?
No. It lumps six precursor groups into one effective group. It is a good estimate for small positive reactivities and a rough one otherwise; detailed work uses the full inhour equation.
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Sources & references
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