原文：https://she-llac.com/claude-limits

主要结论

  1. Claude 订阅计划的“20×”并非整体都翻 20 倍：

    • 5 小时会话额度确实是 Pro 的 20×（11,000,000 credits/5h）。

    • 但周额度只有 Pro 的约 16.67×（83,333,300 credits/week），只比 Max 5× 多约 2 倍。

  2. Max 5× 实际“超额交付”，性价比更高：

    • 5 小时会话额度约为 Pro 的 6×（3,300,000 credits/5h）。

    • 周额度约为 Pro 的 8.33×（41,666,700 credits/week）。

  3. 相比 API 计费，订阅计划价值显著更高，尤其是在缓存读取免费（计划）而 API 对缓存读取按输入的 10% 计费时，循环/多轮工具调用场景下差距会被进一步放大。

判断方法（推断“真实额度”的步骤）

  1. 抓取未四舍五入的使用率（usage ratio）：

    • 使用 Claude.ai 生成接口（SSE）返回的 usage 值，包含未取整的 double，如 0.16327272727272726。

  2. 把 float 还原为分数的“桶”里最简单分数：

    • float 对应某个区间 [L, U)，原始分数一定在这个区间内。

    • 用 Stern-Brocot 树（等价于连续分数）搜索该区间里分母尽量小的分数，得到形如 449/2750 这样的分数。

  3. 用分母最小公倍数得到真实额度：

    • usage = used/limit，分数化简后分母只可能是真实 limit 的因子。

    • 原文核心内容摘录（英文）

      findings

      The 20× plan is not as good of a deal as you might expect. On Anthropic’s site, all mentions of “20× more usage*” have that pesky asterisk. It’s doing a lot of work. The five-hour session limits really are 20× higher than in Pro, but the real question is, how much work can you get out of it? The answer is: only twice as much per week as the 5× plan.

      On the other hand, the 5× plan gives you great value for money. It overdelivers on what it promises pretty significantly. It’s the sweet spot of the pricing table. You get a six times higher session limit than Pro (not five), and more than eight times the weekly limit (more than the eponymous five).

      Credits limits

      Tier

      Credits/5h

      Credits/week

      Pro

      550,000 (1×)

      5,000,000 (1×)

      Max 5×

      3,300,000 (6×)

      41,666,700 (8.33×)

      Max 20×

      11,000,000 (20×)

      83,333,300 (16.67×)

      Compared to API pricing, all plans come out looking fantastic. The value estimates in the table are lower bounds, since caching makes the effective API-equivalent even more favorable (as I’ll explain in a moment). In any case, if you can use plan pricing instead of the API, go for it.

      API cost comparison（Opus 参考）

      Tier

      Price

      Credits/month

      Opus-rate tokens

      Equivalent API cost

      Pro

      $20

      21.7M

      32.5M in or 6.5M out

      $163 (8.1×)

      Max 5×

      $100

      180.6M

      270.9M in or 54.2M out

      $1,354 (13.5×)

      Max 20×

      $200

      361.1M

      541.7M in or 108.3M out

      $2,708 (13.5×)

      There’s one thing that’s not in this table that’s very important.

      Cache reads. They’re entirely free.

      This makes the math even more stacked in favor of the plans. In an agentic loop (e.g. Claude Code), the model makes dozens of tool calls per turn. After every tool call, the model is invoked again. Cache read of the entire context. The API charges 10% for every read; subscriptions charge nothing. This adds up fast, as we’ll see in a second.

      Cache writes are also discounted, they cost 1.25×/2× the input price in the API, while on the plan they’re charged the regular input price. Every chat turn gets written to cache before it can be read, so this matters as well.对多个样本分母取 LCM，当 LCM 稳定后即为真实 limit（例如多个分数共同指向分母 3,300,000）。

  4. 反推 credits-to-tokens 公式（用于把 plan credits 转回 token 量）：

    • credits_used = ceil(input_tokens * input_rate + output_tokens * output_rate)

    • 其中 input/output 的 credit rates 与模型对应，例如：Haiku 入 2/15、出 10/15；Sonnet 入 6/15、出 30/15；Opus 入 10/15、出 50/15。