The optimal spacing interval should expand as memory strength grows, not stay fixed

What it is

Spaced repetition is a scheme for scheduling review or reminder timing, and its core question isn't "how many times to review" but "how the gaps between reviews should be arranged." A common design mistake is a fixed cadence — reminding every three days, forever unchanged. An effective schedule instead uses an expanding interval: each time a memory is successfully recalled, that success signals it has gotten stronger, so the next review should come later than the last gap, not repeat the same fixed period.

Why it happens

Every successful review or retrieval slows the subsequent decay of the corresponding memory trace — not that it will never be forgotten again, but that the window during which it can withstand forgetting has gotten longer. A fixed interval runs into trouble on both ends: early on it may be too long, letting the memory decay noticeably or even partly lapse before review, turning "review" into costly relearning; later on the same interval may be too short, reviewing a memory that's already solid, which is low-yield repeated effort. An expanding interval works better because it ties review timing to the changing quantity of memory strength itself, rather than to a fixed number on a calendar — as strength grows, the safe gap that can be opened up grows with it.

Studying it

The classic design for studying spacing schedules compares fixed, expanding, and contracting review-test cadences at an equal total number of reviews, measuring final retention after days or weeks. One practically useful specific finding: the optimal review interval isn't a fixed multiplier — it scales with the target retention duration. If the goal is to remember something a few days later, intervals should expand on the scale of days; if the goal is to remember it months later, the same expanding logic needs to unfold on the scale of weeks or months — the two goals can't share the same interval parameters.

Where it stops holding

Most of the specific numbers behind these spacing curves come from vocabulary-pair or language-learning app studies; directly transplanting a specific ratio (such as "double the interval after each success") onto interface knowledge or operational steps — content with very different complexity and memorability — hasn't been validated to the same degree. Expanding-interval scheduling also assumes the system can reasonably estimate "how strong this memory is right now," but most real systems lack fine-grained, per-individual strength estimation and instead rely on a rough heuristic formula (double on success, reset to the start on failure) as an approximation — that's a usable approximation, not proof of an optimum validated for that specific content.

Applying it

• If building a reminder or learning feature based on spaced repetition, implement expanding-interval scheduling: each time a user successfully recalls or correctly completes something, extend the interval before the next reminder (doubling it, or growing it by some factor); on any failure, reset the interval back to a short starting point rather than continuing to use the previously expanded value.
• Don't cover all users and all content with one global fixed cadence ("remind once a week") — at minimum, branch the interval based on whether the most recent attempt for that content/user was a success or a failure.
• Validation: A/B test an expanding-interval scheme against a fixed-interval scheme with a comparable total number of reminders, comparing long-term recall or correct-operation rates weeks later — if the expanding-interval group matches or beats retention with a similar or smaller total reminder count, the scheduling itself is doing work.

Related

• Same group: A6.15.2 A prompt or review is most effective right before forgetting occurs, but not after · A6.15.3 Reviewing too early has low marginal benefit because forgetting hasn't yet begun · A6.15.4 Reminder and re-education timing can directly borrow the spaced-repetition scheduling curve
• Nearby: A6.06 Forgetting curve · A6.14 Retrieval from long-term memory
• Search terms: spaced repetition · expanding interval · spacing effect