Free tool · Memory
Forgetting curve calculator
In Ebbinghaus's experiments, relearning a list a day later took about a third less effort than the first time, and a month later about a fifth less. Plot his data, then model how reviews change the curve.
Part 1 · Measured data
What Ebbinghaus measured
Ebbinghaus learned lists of nonsense syllables, waited, then timed how long relearning took. The chart shows how much of the original effort he saved, not how much he remembered. A 2015 replication with one volunteer found a similar curve.
Up: relearning effort saved (%)Across: time since learning (log scale)
- Ebbinghaus, 1880s (measured)
- Murre and Dros, 2015 replication (measured)
- Ebbinghaus's 1885 formula
Show the numbers
| Time since learning | Ebbinghaus (1880s) | Replication (2015) | 1885 formula |
|---|---|---|---|
| 20 minutes | 58.2% | 47.2% | 56.5% |
| 1 hour | 44.2% | 37.3% | 47.1% |
| 9 hours | 35.8% | 27.6% | 34.4% |
| 1 day | 33.7% | 31.7% | 30.4% |
| 2 days | 27.8% | 23.0% | 28.1% |
| 6 days | 25.4% | 16.8% | 24.9% |
| 31 days | 21.1% | 4.1% | 21.2% |
Data: Murre and Dros (2015), PLOS ONE, Table 3, which gives Ebbinghaus's values and their own. Formula: b = 100k ÷ ((log t)^c + k), with k = 1.84 and c = 1.25 and t in minutes (Ebbinghaus, 1885, section 29). One person each time, so treat both curves as examples, not norms.
Part 2 · A model, not data
Model your own reviews
FSRS is an open memory model used for flashcard scheduling. Here it runs with its published default settings, so the curve is an average for flashcard-style facts, not a measurement of you.
Model result (FSRS-6)
96%modelled recall on day 30, with 2 reviews before it
- With no reviews
- 67%
- Reviews before the check day
- days 2 and 14
- Recall stays above 90% after your last review for
- 49 days
- The model's own plan to stay near 90% until day 30
- days 2 and 13
With reviews on days 2 and 14, the model puts recall on day 30 at about 96%, against 67% with no reviews.
Modelled recall, days 0 to 60. Dotted lines mark your reviews and day 30.
- With your reviews
- No reviews
Up: modelled chance of recallAcross: days since first study
Show the numbers
| Day | With your reviews | No reviews | Note |
|---|---|---|---|
| Day 1 | 94.7% | 94.7% | |
| Day 2 | 90.9% | 90.9% | review (value just before it) |
| Day 3 | 98.7% | 88.1% | |
| Day 7 | 94.5% | 80.8% | |
| Day 14 | 89.4% | 74.2% | review (value just before it) |
| Day 21 | 98.0% | 70.2% | |
| Day 30 | 95.8% | 66.8% | check day |
| Day 60 | 90.4% | 60.3% |
To turn review days into calendar dates with a download for your calendar, use the spaced repetition schedule generator.
Runs in your browser. Nothing you type or answer is sent anywhere.
How to use the calculator
The tool has two parts, and they answer different questions.
- Part 1 plots what Ebbinghaus measured. Switch the 2015 replication and his 1885 formula on or off, and open “Show the numbers” for the exact values.
- In part 2, pick how the first study went: “Right first time”, “Hard at first” or “Custom” (you set how many days it takes the modelled recall to fall to 90%).
- Choose a review preset (None, Cram, Spaced or Classic), or type a day into “Add a review on day”. Select a day chip to remove it.
- Set “Check recall after” to the day you care about, such as the day of a test.
- Read the result card and chart. “Show the numbers” lists the values by day, and the CSV button downloads them.
How the numbers are worked out
Ebbinghaus’s data and formula
Ebbinghaus didn’t ask himself what he remembered. He learned a list until he could recite it, waited, then timed how long it took to learn it again. The time he saved, as a share of the first learning time, is called savings. A saving of 34% after a day means relearning took about a third less effort, which is a different thing from remembering a third of the list.
He summed up his results with a formula: b = 100k ÷ ((log t)^c + k), where b is the saving in percent, t is time in minutes and the constants are k = 1.84 and c = 1.25. By his own account he found the constants by “merely approximate estimates”, not by exact fitting. It tracks his data closely. At one day it gives 30.4% against the 33.7% he measured, and at 31 days 21.2% against 21.1%.
The FSRS-6 model
Part 2 uses FSRS, an open model built for flashcard apps, with the FSRS-6 default settings published on the project’s wiki. It predicts the chance you can recall an item after t days:
R = (1 + 0.98 × t ÷ S) raised to the power of minus 0.1542
S is stability, the number of days until the chance of recall falls to 90%. After a first study you got right, the default stability is 2.3065 days. Each successful review raises stability, and it rises more when the review comes later, once recall has dropped a little. The tool assumes every review is answered correctly.
With the defaults (right first time, reviews on days 2 and 14, check on day 30), the model gives about 96% recall on day 30, against about 67% with no reviews. Move the reviews to days 1, 2 and 3 and the day 30 figure drops to about 86%. By day 60 the gap is wider: about 90% for the two spaced reviews against about 80% for the three crammed ones (our calculation).
What Ebbinghaus measured
Ebbinghaus was his own subject. In 1879 and 1880 he learned series of 13 nonsense syllables and ran 163 pairs of learning and relearning sessions. These are his savings, as tabulated by Murre and Dros in 2015, next to their replication:
| Time since learning | Ebbinghaus (1880s) | Replication (2015) |
|---|---|---|
| 20 minutes | 58.2% | 47.2% |
| 1 hour | 44.2% | 37.3% |
| 9 hours | 35.8% | 27.6% |
| 1 day | 33.7% | 31.7% |
| 2 days | 27.8% | 23.0% |
| 6 days | 25.4% | 16.8% |
| 31 days | 21.1% | 4.1% |
Nonsense syllables were the point. He wanted material with no meaning to lean on, so the curve shows forgetting at its plainest. Material that means something to you may fade at a different rate, which is one reason the chart can’t predict your own memory.
The 2015 replication
Murre and Dros (2015) repeated the method with one volunteer, the second author, across the same seven delays. They concluded that the curve “has indeed been replicated”, and found it most probably jumps upward at the 24-hour point. You can see that bump in the chart: savings at one day are higher than at nine hours. The authors suggest sleep as a possible reason and say the idea needs testing. The replication’s 31-day value (4.1%) is unusually low, which they link to a compressed schedule.
What slows forgetting
A 2013 review of 10 study techniques rated only two as high utility: practice testing and spacing out study.
On spacing, a 2006 review of 317 experiments, covering 839 assessments of distributed practice, found that the best gap between study sessions gets longer the longer you need to remember the material. On testing, students in a 2006 experiment by Roediger and Karpicke who took a recall test instead of rereading a passage remembered 56% of it a week later, against 42% for those who reread it. After five minutes, rereading won (81% against 75%), so a quick check straight after studying can flatter rereading.
To turn review days into calendar dates, the spaced repetition schedule generator plans them from a start date and a test date and gives you a calendar file. For a longer read on the curve itself, see the forgetting curve guide.
What the result doesn’t tell you
The model is an average for flashcard-style items, run with default settings that haven’t been tuned to anyone in particular. It assumes you answer every review correctly. It can’t see how well you understood the material, how much you slept or how the test will ask the question, and all of those move real recall. Read its percentages as a comparison between schedules, not a forecast for you.
The data chart has its own limits. Two people, each learning nonsense syllables, and a measure (savings) that isn’t the share remembered. They show the shape of forgetting under lab conditions, which is why the two parts of the tool sit on separate charts.
Forgetting curve calculator: common questions
What is the Ebbinghaus forgetting curve?
It's a graph of how much effort Hermann Ebbinghaus saved when he relearned lists of nonsense syllables after delays from 20 minutes to 31 days. The saving fell fast at first (about 58% after 20 minutes, 34% after a day) and slowly after that (21% after a month). He was the only subject, and the curve shows relearning effort saved, not the share he remembered.
What is the forgetting curve formula?
Ebbinghaus's own formula was b = 100k ÷ ((log t)^c + k), with k = 1.84 and c = 1.25, where b is the saving in percent and t is time in minutes. He said he set the constants by approximate estimates, not exact fitting. Modern models such as FSRS use a power curve for the chance of recall, which falls to 90% after S days, where S is the memory's stability.
How fast do we forget?
It depends on the material and how well you learned it. With nonsense syllables, Ebbinghaus's relearning savings fell to about a third after a day and a fifth after a month. For an average flashcard answered correctly once, the FSRS-6 model with default settings puts the chance of recall at about 81% after a week and 67% after a month (our calculation).
How do reviews change the forgetting curve?
Each successful review makes the modelled memory more stable, so the next drop is slower. In the FSRS-6 model, reviews on days 2 and 14 give about 90% recall on day 60, against about 80% for three crammed reviews on days 1, 2 and 3, and about 60% with none (our calculation). Experiments on spacing and self-testing point the same way.
Has the forgetting curve been replicated?
Yes. In 2015 Murre and Dros repeated Ebbinghaus's method with one volunteer over the same seven delays and got a very similar curve, with a small upturn at the 24-hour point that they think may reflect sleep. It was one person again, so it confirms the shape of the curve, not a rule for everyone.
Related tools
- Spaced repetition scheduleWhen to review something so you remember it by a date, with a calendar file.
- Memory test (digit span)How many digits you can hold in mind, forward and backward.
- Reading speed testYour words per minute on a real passage, with a comprehension check.
Guides
- What the forgetting curve shows, and what to do about itEbbinghaus's forgetting curve from his own data and a 2015 replication: what 'savings' measures, how fast we forget, and what spaced reviews and self-testing add.
- How to remember what you readRecall a chapter before you reread it, write one sentence from memory and review it days later. What the reading research supports, and why highlighting rates low.