Vocabulary Retention Rate Estimator

Why Vocabulary Fades Over Time

After you first learn a new word, your memory for it is relatively fragile. If you do not encounter or review that word again, your ability to recall it drops quickly at first and then more slowly. This pattern is often described by the forgetting curve.

In broad terms:

• Without review, recall falls sharply in the first days.
• Each successful review makes the memory more stable and slows the rate of forgetting.
• Spaced repetition takes advantage of this by reviewing words just before you are likely to forget them.

The estimator on this page uses a mathematical model that captures this kind of decline in a very simplified way. It assumes that you retain the same fraction of your vocabulary from one day to the next, which leads to an exponential decay curve.

The Exponential Decay Formula

The calculator estimates how many words you still remember using an exponential decay formula:

Formula (in plain notation):

R = W × (p / 100)d

Where:

• R = estimated number of words remembered now
• W = number of words originally studied
• p = daily retention percentage (for example, 90 means 90% per day)
• d = days since your last review of those words

Written in mathematical markup, the same relationship looks like this:

Intuitively, p / 100 is the fraction of words you keep from one day to the next. Raising this fraction to the power d applies that same decay repeatedly over d days.

How to Interpret the Inputs

Words Studied (W)

Enter the number of vocabulary items you originally learned in the relevant study session or time period. This might be:

• New words from a single textbook chapter
• An entire flashcard deck you last reviewed on the same day
• A batch of words you crammed the night before an exam

You can use any realistic number, from a handful of words to several thousand. The model treats each word as equally likely to be remembered, which is one of its simplifications.

Days Since Last Review (d)

This is the number of complete days that have passed since you last practiced or reviewed those specific words in a meaningful way. Rough guidelines:

• 0 days means you are estimating immediately after study (you should remember almost all of them).
• 1–3 days reflects very recent study with some early forgetting.
• 7+ days lets you see how quickly things drop off without review.

Daily Retention Percentage (p)

The daily retention percentage is the average proportion of words you retain from one day to the next. A higher value means slower forgetting. For example:

• 95% = you keep 95% of what you knew the previous day.
• 90% = you keep 90%, losing about 10% per day.
• 80% = you keep 80%, losing about 20% per day.

If you are unsure what to use, start with 90% as a reasonably optimistic, but not perfect, assumption. You can then adjust it up or down based on your experience. If you feel you forget faster than expected, try a lower percentage.

Worked Example

Imagine you learned 50 new vocabulary words and you want to estimate how many you still remember 3 days later. You believe your daily retention is about 90%.

1. Start with the words studied:
   W = 50
2. Convert the daily retention percentage to a decimal:
   p = 90% becomes p / 100 = 0.90
3. Apply the decay over 3 days:
   (0.90)3 = 0.9 × 0.9 × 0.9 = 0.729
4. Multiply by the original word count:
   R = 50 × 0.729 = 36.45

The model predicts that you will remember roughly 36 out of 50 words after three days without review. The calculator does the arithmetic instantly, so you can focus on interpreting what that number means for your study plan.

Interpreting Your Result

The output of the estimator is the estimated number of words remembered. You can think of it in a few practical ways:

• As a percentage of your original effort: If you studied 200 words and the estimator returns 120, that means you are likely to recall about 60% of that batch.
• As a guide for review timing: If the predicted retained count has dropped lower than you would like, that is a signal to review those words before they fade further.
• As a way to prioritize: If you have several decks or chapters, you can compare which ones have decayed the most and review the weakest first.

Remember that this is an average estimate, not a guarantee for every single word. In reality, you will remember some difficult words less well and some frequently used words far better than the model suggests.

Comparison Table: How Retention Drops Over Time

The table below shows how many words you might remember from an initial set of 100 words under different daily retention rates and review delays.

You can read the table row by row:

• With a 95% daily retention rate, you still remember about 60 of the 100 words after 10 days without review. Forgetting is fairly gradual.
• At 90%, only about 35 words remain after 10 days. That is a much steeper decline.
• At 80%, retention collapses quickly: you remember only about 11 of the 100 words after 10 days.

This illustrates how sensitive vocabulary retention is to both your personal forgetting rate and the delay before you review. Even small improvements in daily retention (for example, by using better study methods) can significantly increase how much vocabulary you retain over a week or two.

How to Use This Estimator in Your Study Plan

1. Estimate your current retention: Enter your recent study session (for example, 80 words, 4 days ago, 90% daily retention) and see how many words the model thinks you still know.
2. Adjust your review intervals: If the estimated retained count is lower than you are comfortable with, shorten the time between reviews for similar material.
3. Tune your daily retention rate: Compare the estimates with your actual experience. If you usually score lower than predicted on quizzes, try a lower daily retention percentage; if you do much better, try a higher one.
4. Plan ahead: Use future days in the calculator to forecast how many words you might remember by the time of an exam or trip, and schedule extra reviews if needed.

Assumptions and Limitations

This vocabulary retention estimator is intentionally simple. It is designed to be easy to understand and fast to use, not to capture every nuance of human memory. It relies on several important assumptions:

• Constant daily retention rate: The model assumes you retain the same percentage of words each day. In reality, forgetting is often faster immediately after learning and slower later on.
• Independent words of equal difficulty: Every word is treated as equally likely to be remembered or forgotten. Real vocabulary varies widely in difficulty and exposure.
• No intermediate reviews or exposure: The days since last review are assumed to be days without meaningful practice. Casual exposure to words in reading, listening, or conversation can reinforce them and improve actual retention.
• Single study event: The formula is applied to one batch of words learned or reviewed at the same time, not to a complex history of many smaller reviews.

Because of these assumptions, you should treat the results as estimates, not guarantees. They are most useful for:

• Comparing different scenarios (for example, reviewing every 3 days vs. every 7 days).
• Developing intuition about how quickly vocabulary can fade.
• Setting conservative review schedules to avoid unpleasant surprises.

If you are using a dedicated spaced repetition system, its built-in algorithms usually track your performance word by word and can adaptively adjust intervals more precisely than this generic model. You can still use this estimator as a mental check on how aggressive or conservative your review strategy is.

Practical Retention Strategies

To improve your real-world vocabulary retention beyond what any simple model predicts, combine the estimator with proven learning techniques:

• Spaced repetition: Review words at increasing intervals instead of cramming. This strengthens long-term memory efficiently.
• Active recall: Test yourself by trying to produce the meaning or translation from memory, rather than just rereading lists.
• Use words in context: Write sentences, speak with a partner, or read and listen to materials that include your target vocabulary.
• Mix old and new words: Each session, revisit a subset of older vocabulary alongside fresh items to keep your foundation solid.

As you adjust your habits, you may notice that your actual forgetting is slower than before. At that point, you can experiment with higher daily retention values in the estimator to reflect your improved learning efficiency.