All calculatorsForgetting Curve Calculator
Estimate recall probability over time and get a recommended next review using a simple, research-inspired forgetting curve model. Choose a mode, enter a few inputs, and see results with optional step-by-step and a mini visualization.
Background
The forgetting curve describes how memory fades over time without review—an effect first studied by Hermann Ebbinghaus. A common way to model this is an exponential decay where retention drops as time passes. Reviewing the material boosts memory and increases the time it takes to forget again (that’s the basic idea behind spaced repetition).
How to use this calculator
- Pick a mode: Recall, Next Review, or Exam Schedule.
- Enter your inputs (time, difficulty, reviews, target retention).
- Click Calculate to see retention estimates + optional steps.
How this calculator works
- We model retention using an exponential forgetting curve: R(t) = R₀ · e^(−t/τ)
- τ (memory time constant) grows with more reviews and easier material.
- To find a next review time for a target retention R*, we solve: t = −τ · ln(R*/R₀)
Formula & Equation Used
Retention model: R(t) = R₀ · e^(−t/τ)
Next review time: t_next = −τ · ln(R_target / R₀)
Example Problem & Step-by-Step Solution
Example 1 — Recall after 24 hours
You last reviewed a concept 24 hours ago. It’s medium difficulty and you’ve completed 1 review. Starting mastery is 90%.
- Use retention model: R(t) = R₀ · e^(−t/τ)
- Convert inputs: R₀ = 0.90, t = 24 h
- Compute τ from difficulty + reviews (model choice)
- Compute R(t) and output recall probability
Example 2 — Next review time to stay ≥ 85%
You want to keep recall at or above 85%. The topic is medium difficulty, you’ve completed 2 reviews, and your starting mastery is 92%.
- Use planner equation: t_next = −τ · ln(R_target / R₀)
- Convert inputs: R₀ = 0.92, R_target = 0.85
- Compute τ from difficulty + number of reviews
- Solve for t_next and display as hours + days
Example 3 — Recall after 5 days (hard topic)
You last reviewed a hard concept 5 days ago. You’ve completed 1 review and your starting mastery is 88%.
- Use retention model: R(t) = R₀ · e^(−t/τ)
- Convert time: t = 5 days (convert to hours internally)
- Compute τ from difficulty + reviews
- Compute R(t) and output recall probability
Frequently Asked Questions
Q: Is this exact?
No. Real memory varies by person and topic. This calculator provides a reasonable, educational estimate and a practical review suggestion.
Q: Why do more reviews help?
Reviewing strengthens retrieval and typically increases the time it takes to forget again, which is the key idea behind spaced repetition.
Q: What’s “starting mastery”?
It’s your estimated retention immediately after your last review. If you’re unsure, leave it blank and we’ll use a default based on difficulty.
Q: Can I use this for flashcards?
Yes — flashcards are a great fit because each review is a retrieval attempt and spacing matters.