> For AI agents: the complete documentation index is available at https://open-spaced-repetition.github.io/ts-fsrs/llms.txt, the full documentation bundle is available at https://open-spaced-repetition.github.io/ts-fsrs/llms-full.txt.

# FSRS-6

FSRS-6 has 21 trainable weights, including a trainable forgetting-curve decay and a same-day stability term.

See the [Model overview](https://open-spaced-repetition.github.io/ts-fsrs/guide/model.md) for the shared symbols and Model contract.

:::info Formula source
Reviewed against [awesome-fsrs Wiki — FSRS-6](https://github.com/open-spaced-repetition/awesome-fsrs/wiki/The-Algorithm#fsrs-6).
:::

## Forgetting curve and interval

With the positive decay magnitude `math:d = w_{20}`, choose `math:F` so that `math:R(S, S) = 0.9`:

```math
F=0.9^{-1/d}-1,\qquad
R(t,S)=\left(1+F\frac{t}{S}\right)^{-d}
```

```math
I(r,S)=\frac{S}{F}\left(r^{-1/d}-1\right)
```

`nextInterval` rounds the result to whole days and returns at least one day.

## Initial memory

```math
S_0(G)=\operatorname{clamp}\left(w_{G-1},S_{min},S_{max}\right)
```

```math
D_0(G)=w_4-e^{w_5(G-1)}+1,\qquad
D_{initial}=\operatorname{clamp}\left(D_0(G),1,10\right)
```

## Difficulty

```math
\Delta D=-w_6(G-3),\qquad
D^*=D+\Delta D\frac{10-D}{9}
```

```math
D'=\operatorname{clamp}\left(w_7D_0(4)+(1-w_7)D^*,1,10\right)
```

## Stability after review

For `math:t > 0`, or when `enableShortTerm` is disabled, the rating selects the following branch.

The update uses the pre-review `math:D` and `math:S`. `math:H_G = w_{15}` for Hard and `math:1` otherwise; `math:E_G = w_{16}` for Easy and `math:1` otherwise.

When `enableShortTerm` is enabled, `math:C` is the previous stability multiplied by `math:\exp(-w_{17}w_{18})`; otherwise, `math:C = S`:

```math
S_f=\min\left(w_{11}D^{-w_{12}}\left((S+1)^{w_{13}}-1\right)e^{w_{14}(1-R)},C\right)
```

```math
S_r=S\left[1+e^{w_8}(11-D)S^{-w_9}\left(e^{w_{10}(1-R)}-1\right)H_GE_G\right]
```

```math
S'_{raw}(G)=
\begin{cases}
S_f,&G=1\\
S_r,&G\in\{2,3,4\}
\end{cases}
```

`math:C` is an implementation cap for post-lapse stability, not a separately configured stability floor. The model then clamps `math:S'_{\mathrm{raw}}` to the range from `math:S_{\min}` to `math:S_{\max}`.

## Same-day update

Here, “same-day” means the model receives `elapsedDays = 0`; the model does not inspect calendar dates. Direct callers and the scheduler’s `chrono` determine the elapsed value.

When `enableShortTerm` is enabled and `math:t = 0`:

```math
s_{inc}=S^{-w_{19}}e^{w_{17}(G-3+w_{18})}
```

```math
S'=\operatorname{clamp}\left(Sm,S_{min},S_{max}\right),
\qquad
m=\begin{cases}
s_{inc},&G=1\\
\max(s_{inc},1),&G\ge2
\end{cases}
```

Hard, Good, and Easy cannot reduce stability below its current value; Again may reduce it.