Scientific Analysis

Spaced Repetition & the Power of the SM-2 Algorithm

Learning is strengthening a connection built by the brain; forgetting is a biological economy. The SuperMemo-2 (SM-2) algorithm calculates the exact moment information fades from memory, enabling permanent learning.

Bending the Forgetting Curve

In 1885, Hermann Ebbinghaus researched how the human brain forgets newly learned information. The result was striking: We forget 80% of what we learn within the first 48 hours.

However, if information is reviewed just as it is about to be forgotten (e.g., when the memory retention drops to 10-20%), the brain thinks this information is vital and rebuilds the synaptic connection much stronger. Each spaced repetition slows down the forgetting rate; meaning it bends the curve, transferring it to long-term memory.

90% Time Savings: You avoid unnecessary repetitions and study only at the boundary of forgetting.
Active Recall Bridge: It exercises the brain's recall muscles, making learning permanent.

Traditional Cramming vs. SM-2 Algorithm

Traditional Cramming

Reading words for hours on the night before an exam or on a single day. Information is quickly piled into short-term memory and 90% of it is completely forgotten after 3 days.

SM-2 Spaced Repetition

A word is reviewed for just 10 seconds only at forgetting thresholds: on Day 1, Day 6, Day 15, and Day 35. Permanent learning is achieved with minimal effort for a lifetime.

Interactive Experiment Station

SM-2 Algorithm Simulator

Change memory parameters with the tool below to watch in real-time how the brain's retention rate changes over 30 days and how reviews reset the waves of forgetting.

Modify Values & Watch the Curve

4 - Correct with Hesitation

Correct recall after a short hesitation.

As you increase the repetition count, watch how the purple curve's decay rate slows down (almost flattening). This is proof of the information settling into long-term memory.

Next Interval

1 Days

New Easiness Factor (EF)

2.5

Repetition Progress

#1

Memory Retention Rate (%) / Time Chart

%0%25%50%75%1000 d5 d10 d15 d20 d25 d30 dLearningReview #1Review #2Review #3
SM-2 Spaced Repetition (Consistent 80%+ Recall)
Classic Forgetting Curve Without Repetition

Review Days According to the 30-Day Plan

Today's SessionStart
Repetition #1+6 Days
Repetition #2+12 Days
Repetition #3+27 Days

Mathematical Rules of the Algorithm

1️⃣

Interval Formula

The first review is after 1 day, the second after 6 days. For subsequent reviews (n > 2), the new interval is calculated by multiplying the previous interval by the Easiness Factor (EF).

I(1) = 1 day
I(2) = 6 days
n > 2: I(n) = I(n-1) * EF
2️⃣

Easiness Factor (EF)

Represents the difficulty of learning a card. The default value is 2.50. Based on your quality of recall, the factor increases (interval lengthens) or decreases (reviewed more frequently).

EF' = EF + (0.1 - (5 - q) *
(0.08 + (5 - q) * 0.02))
3️⃣

Reset Condition

If the rating given by the user is below 3 (q < 3), meaning the information was not recalled correctly, the repetition count (n) is reset to 0, returning the card to Day 1. The EF is decreased.

q < 3 ise:
n = 0 (Learning Phase)
Sonraki Aralık = 1 Day

Neurobiology of Memory Consolidation and Spaced Repetition

Learning and memory processes in the human brain occur through the strengthening of connections between neurons, a biological process known as Long-Term Potentiation (LTP). When information is first acquired, it triggers transient electrical activity. Without reinforcement, the chemical receptors at the synapses rapidly decay, leading to memory loss. This is described by Hermann Ebbinghaus's famous "Forgetting Curve," which shows that approximately 80% of new information is lost within the first 48 hours if no reviews occur.

Spaced Repetition exploits this biological mechanism. Rather than studying continuously (cramming), which only overloads working memory, it schedules reviews at the precise moment of near-forgetting (when retrievability drops to 10-20%). Forcing the brain to engage in **Active Recall** under these conditions triggers neural signaling that restructures synaptic pathways, accelerating the transfer of data from the hippocampus (short-term memory) to the neocortex (long-term memory).

The SuperMemo-2 (SM-2) algorithm models this neurobiological consolidation mathematically. Based on the user's response quality (0-5 rating, q), the Easiness Factor (EF)is recalculated. High-quality answers (q = 5) cause subsequent intervals to grow exponentially, while low-quality recalls (q < 3) reset the repetition cycle back to the learning phase. This ensures study times are minimized while long-term retention metrics are optimized.

This Algorithm is the Heart of Polyvo

We explored the spaced repetition algorithm at the code level and saw its impact on charts. Our language learning app, Polyvo, schedules all your vocabulary decks using these SM-2 formulas. You just learn; let Polyvo think about when to review.

Try Polyvo on the Web