Cross-Section and Luminosity Calculator

Luminosity is a measure of how many particle collisions per unit time per unit cross-sectional area a collider delivers, typically expressed in units of cm⁻²s⁻¹ (instantaneous luminosity). Higher luminosity means more collisions and more data for a given process.

A cross-section σ quantifies how likely a specific physics process (like producing a particular particle) is to occur in a collision, expressed in area units (commonly barns and their sub-units). A larger cross-section means the process happens more often for the same luminosity.

Rate = L × σ, where L is the instantaneous luminosity (cm⁻²s⁻¹) and σ is the cross-section (converted to cm²). Multiplying by the running time gives the total expected number of events.

A barn (10⁻²⁴ cm²) is the traditional unit of cross-section in nuclear and particle physics, roughly the geometric size of a uranium nucleus. It was named because such nuclear cross-sections seemed 'as big as a barn' compared to the vastly smaller cross-sections typical in particle collisions.

Rare processes like Higgs boson production have cross-sections in the tens of picobarns (10⁻¹² barn) or smaller, and integrated luminosity is often quoted in inverse femtobarns (fb⁻¹). This calculator supports mb, μb, nb, pb, and fb alongside the base barn unit.

The LHC's design instantaneous luminosity is about 10³⁴ cm⁻²s⁻¹, one of the highest ever achieved in a particle collider, enabling the discovery of the Higgs boson (with a production cross-section of tens of picobarns) within a few years of data-taking.

Total events = Rate × running time, this calculator multiplies the computed rate by your chosen running time (converted to seconds) to give the expected total event count, useful for estimating how much data a given process will accumulate.

Since Rate = L × σ, a process with a very small cross-section (like Higgs production) needs a correspondingly large luminosity to produce a usable event rate. This is the central engineering driver behind pushing collider luminosity ever higher, exactly why the LHC's High-Luminosity upgrade targets roughly 5-10 times the original design luminosity.

No, this calculator computes the theoretical physics event rate (Rate = L × σ) only. Real experiments must further multiply by detector acceptance and trigger efficiency to estimate how many events are actually recorded, which this calculator does not include.

Integrated luminosity is the luminosity accumulated over a running period (∫L dt, in units like fb⁻¹), and total events = σ × integrated luminosity. This calculator computes the equivalent result by multiplying the instantaneous rate by your chosen running time.