Multi-Stage Flotation Circuit Calculator
Model a sequential flotation circuit — rougher/scavenger (tail-to-next) or cleaner (concentrate-to-next) — to get incremental and overall recovery and the combined concentrate grade, without pretending to be a recycle-loop simulator.
Stages
| Stage | Recovery % | Mass pull % | |
|---|---|---|---|
Recovery is the fraction of metal ENTERING each stage. Recycle loops need measured reconciliation, not a serial formula.
Circuit result
Everything runs in your browser. Inputs are never saved or transmitted.
- Add at least one stage with a recovery.
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Choose the circuit type: tail-to-next (rougher/scavenger) or concentrate-to-next (cleaner).
- Add a row per stage with its recovery (of the metal entering that stage) and, optionally, its mass pull.
- Read the cumulative recovery after each stage, the overall recovery and the combined concentrate grade.
How it works
In a tail-to-next circuit each stage recovers a fraction rᵢ of the metal still in the previous stage's tail, so the overall recovery is 1 − ∏(1 − rᵢ). In a cleaner (concentrate-to-next) circuit each stage upgrades the previous concentrate, so the recovery relative to the original feed is the product of the stage recoveries ∏rᵢ. Stage concentrate grade needs the stage mass pull; the combined product grade is total recovered metal ÷ total concentrate mass.
This is a transparent sequential balance, not a full simulator. Closed recycle loops (e.g. cleaner tails returning to the rougher) cannot be solved by a serial formula — they need measured-stream reconciliation. The tool keeps recovery-of-entering-metal, cumulative recovery and mass pull clearly distinct so the numbers can't be quietly conflated.
Worked example
Rougher then scavenger. A rougher recovers 70% of the feed metal; the scavenger then recovers 40% of the metal remaining in the rougher tail. Overall recovery = 1 − (1 − 0.70)(1 − 0.40) = 1 − 0.30 × 0.60 = 82.0%.
Common mistakes
- Adding stage recoveries directly — they compound on the remaining metal, they don't sum.
- Confusing recovery of entering metal with cumulative recovery of the original feed.
- Modelling a recycle loop with this serial tool; use measured reconciliation instead.
Frequently asked questions
Why isn't 70% + 40% equal to 110%?
The scavenger only sees the 30% of metal the rougher left behind, so it adds 40% of that 30% (12 points), giving 82% overall — never more than 100%.
Can it handle recycle streams?
No — closed loops need a measured-stream mass balance or a validated solver. This tool models open sequential stages transparently and says so.
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Cite this tool
Zerdly. (2026). Multi-Stage Flotation Circuit Calculator. Retrieved from https://www.zerdly.com/tools/multi-stage-flotation-circuit-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.