Deep Work Capacity · Focus Horizon
Exponential focus decay, e^(−0.01×min) · half-life ≈ 69 min · floor at 0.
Focus is not steady — it decays exponentially from the moment you start. Quality = 100 × e^(−0.01 × min), floor at 0. Half-life ≈ 69 min. After that every additional unit of time delivers half the output. The tail is where you make typos and bugs.
Part of: Cognitive Throughput
How to use
- Enter minutes of continuous focused work so far.
- Quality = 100 × e^(−0.01 × min), capped at 0.
- Above 70% = Peak_Focus · 15–40% = Decaying · below 3% = Focus_Collapse.
- Horizon shows time left before quality drops below 15% — take the break at that marker, not after.
Examples
Before you act on the result
Logic tools help expose a tradeoff, but they cannot see the full situation around the decision. Use the result to slow down the choice and name the assumption that matters most.
If one input drives the answer, test that assumption before treating the result as stable.
Next up
Frequently asked questions
› Does everyone decay at the same rate?
No. λ varies by person, sleep, and task difficulty. 0.01/min is a rough baseline — adjust mentally if you know yours is flatter or steeper.
› Why cap at 0? Troubleshooting
Exponential decay never reaches 0 mathematically, but focus quality below ~3% is operationally dead. The cap prevents misleading "2% focus" readouts that suggest you are still working.
Tips & related reading
See the Cognitive Throughput hub →Tips & how-tos
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Signal-to-Noise · Content Throughput
Measure how much of your daily information intake converts into actionable decisions. Throughput-pipe visual with clogged / flowing state.