Ebbinghaus Forgetting Curve R = exp(−t/S) & SuperMemo SM-2 Interval Calculator

Compute Ebbinghaus memory retrievability R(t) and SuperMemo SM-2 / FSRS spaced repetition intervals.

Current Memory Retrievability R(t)
75.148 %
Next Optimal SM-2 Review Interval 35 days
Updated SM-2 Easiness Factor (EF′) 2.5 EF
Optimal Day to Review at 90% Retention 1.475 day
Inputs
⚡ Scenarios:
days
Current memory stability S in days (time for retention to decay to 1/e ≈ 36.8%).
days
Days elapsed since last active recall review (t).
EF
Current SM-2 card Easiness Factor (1.30 hardest to 2.50+ easiest).
0–5 grade
Self-graded recall quality q (5 = instant, 4 = correct after hesitation, 3 = hard correct, <3 = lapse).
Results & Graph
Current Memory Retrievability R(t)
75.148 %
Next Optimal SM-2 Review Interval
35 days
Updated SM-2 Easiness Factor (EF′)
2.5 EF
Optimal Day to Review at 90% Retention
1.475 day

Current Memory Retrievability R(t)

Graph 1 • Forgetting Curve & SM-2 Interval • Domain Architecture & Live Telemetry Maps Memory Stability Days S, Elapsed Days Since Review T, Current Easiness Factor Ef through Forgetting Curve & SM-2 Interval Formula.
Current Memory Retrievability : 75.148 % Forgetting Curve & SM-2 Interval • Invariants & Metrics Current Memory Retrievabilit 75.148 % Next Optimal SM-2 Review Int 35 days Updated SM-2 Easiness Factor 2.5 EF Optimal Day to Review at 90% 1.475 day
Graph 2 • Current Memory Retrievability R(t) Across Memory Stability Days S Sweep (40% → 160%) Evaluates Retrievability R(t) = exp(−t / Stability_S); EF′ = EF + [0.1 − (5 − q) across 7 operating points (current input highlighted).
0 % 46.01 % 92.01 % 48.95 5.60days 62.12 8.40days 69.97 11.20days 75.15 14days 78.81 16.80days 81.54 19.60days 83.65 22.40days
Graph 3 • Joint Sensitivity: Memory Stability Days S × Elapsed Days Since Review T Compares Current Memory Retrievability R(t) when Elapsed Days Since Review T is shifted +25% (solid) vs. −25% (dashed).
0 % 46.64 % 93.28 % --- Elapsed Days Since Review T @ 75% 60.04 -30% 65.69 -15% 69.97 +0% 73.30 +15% 75.98 +30%
Summary: After 4 days at stability S=14 days, recall probability is 75.1% (90% review point = day 1.5); grading q=4 updates SM-2 Easiness Factor to 2.5 and schedules the next review in 35 days.
Summary: After 4 days at stability S=14 days, recall probability is 75.1% (90% review point = day 1.5); grading q=4 updates SM-2 Easiness Factor to 2.5 and schedules the next review in 35 days.
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Formula & Mathematical Methodology: Forgetting Curve & SM-2 Interval Formula

Retrievability R(t) = exp(−t / StabilityS)
EF′ = EF + [0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)]
NextInterval = PrevInterval × EF′
Retrievability R(t) = exp(−t / Stability_S); EF′ = EF + [0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)]; NextInterval = PrevInterval × EF′
  • memoryStabilityDaysS: Current memory stability S in days (time for retention to decay to 1/e ≈ 36.8%).
  • elapsedDaysSinceReviewT: Days elapsed since last active recall review (t).
  • currentEasinessFactorEf: Current SM-2 card Easiness Factor (1.30 hardest to 2.50+ easiest).
  • recallQualityGrade0to5: Self-graded recall quality q (5 = instant, 4 = correct after hesitation, 3 = hard correct, <3 = lapse).

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Forgetting Curve & SM-2 Interval Worked Example

Compute Ebbinghaus memory retrievability R(t) and SuperMemo SM-2 / FSRS spaced repetition intervals.

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: Retrievability R(t) = exp(−t / Stability_S); EF′ = EF + [0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)]; NextInterval = PrevInterval × EF′.
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Forgetting Curve & SM-2 Interval via Retrievability R(t) = exp(−t / Stability_S); EF′ = EF + [0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)]; NextInterval = PrevInterval × EF′.

Frequently Asked Questions

How does the Ebbinghaus Forgetting Curve R = exp(−t/S) & SuperMemo SM-2 Interval Calculator perform the calculation?

It evaluates Retrievability R(t) = exp(−t / Stability_S); EF′ = EF + [0.1 − (5 − q) × (0.08 + (5 − q) × 0.02)]; NextInterval = PrevInterval × EF′ directly in your browser and renders three custom SVG charts in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this tool work offline?

Yes. All calculations run 100% locally in your browser with full offline PWA support.

Education · Study Planning & Cognitive Science

Ebbinghaus Forgetting Curve R = exp(−t/S) & SuperMemo SM-2 Interval Calculator: inputs, method, and how to read the result

Compute Ebbinghaus memory retrievability R(t) and SuperMemo SM-2 / FSRS spaced repetition intervals.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Memory Stability Days S: Current memory stability S in days (time for retention to decay to 1/e ≈ 36.8%).
  • Elapsed Days Since Review T: Days elapsed since last active recall review (t).
  • Current Easiness Factor Ef: Current SM-2 card Easiness Factor (1.30 hardest to 2.50+ easiest).
  • Recall Quality Grade0to5: Self-graded recall quality q (5 = instant, 4 = correct after hesitation, 3 = hard correct, <3 = lapse).

What the calculation includes

With the default values shown, Current Memory Retrievability R(t) is 75.148 %. The calculation follows Forgetting Curve & SM-2 Interval Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Memory Stability Days S from 14 days to 15.4 days changes Current Memory Retrievability R(t) from 75.148 % to 77.125 %. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official NIST Special Publication 811, IEEE/RFC systems engineering, APA psychometric, and USNO astronomical formulas.
  • Empirical metallurgy and calendar conversions represent standard reference-condition approximations.

Scope: Global NIST, IEEE, APA & Astronomical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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