What base are OpenAI logprobs in — natural log or log2?

OpenAI (and Azure OpenAI, vLLM, and llama.cpp) return logprobs in natural log — base e. So a probability is exp(logprob), not 2^logprob. This calculator uses natural log by default; switch the log base only if your framework documents log2 or log10.

How do I convert a logprob to a percentage confidence?

Take e to the power of the logprob, then multiply by 100. For example logprob -0.22 gives exp(-0.22) = 0.8025, which is 80.25%. A logprob of 0 is 100% (the model was certain); very negative logprobs approach 0%.

What does a logprob of 0 mean?

A logprob of 0 means exp(0) = 1, i.e. 100% probability — the model assigned all of its probability mass to that token. In practice you rarely see an exact 0; you see values like -0.0001, which round to 99.99%. A positive logprob is impossible and signals a sign or parsing error.

Can logprobs detect hallucinations or low-confidence tokens?

They are a useful heuristic, not a guarantee. A low token probability flags where the model hesitated, which often correlates with errors — but a model can also be confidently wrong. Use the low-confidence flag to prioritise review, not as a calibrated hallucination detector.

How do I get the probability of a whole sentence from token logprobs?

Sum the token logprobs, then exponentiate: joint probability P = exp(Σ logprob). This equals the product of the per-token probabilities by the chain rule of probability. Because it multiplies many values below 1, the joint probability of a long output is naturally small — that is expected, not a bug.

What is perplexity and how is it computed here?

Perplexity is exp(-mean logprob) = P^(-1/N), the effective number of equally-likely choices the model faced per token. Lower is more confident: 1.0 is perfect certainty. This tool computes it both ways and cross-checks that they agree, so you can trust the number.

Why don't the top alternative tokens add up to 100%?

The top_logprobs field returns only the top-k candidates (up to 20), not the whole vocabulary. Their probabilities are correct individually but are a truncated slice of the full distribution, so they sum to less than 100%. The rest of the mass is spread across thousands of other tokens.

Does this tool send my data to any server?

No. Everything runs in your browser with plain arithmetic — no API key, no upload, no request. You can paste logprobs from private or production responses safely, and the page works offline once loaded.

It accepts a raw OpenAI response — what exactly can I paste?

In JSON mode you can paste the full chat completion, a single choice, a logprobs object, or a bare content array. It also reads the legacy completions shape (token_logprobs/tokens) and a plain array of numbers. Non-numeric fragments are skipped with a note rather than failing.

AI · Developer

AI Logprob to Probability Calculator (Token Confidence)

Paste a logprob, a list, or a raw OpenAI logprobs response and read the probability, per-token confidence %, the joint sequence probability and perplexity. Natural-log by default, runs in your browser, no API key — sources cited below.

By Induwara Ashinsana— Executive Director, Ryzera TechnologiesUpdated Jul 9, 2026

Logprob → probability

Log base

OpenAI, Azure, vLLM default

Logprob value

A valid logprob is 0 or negative. Paste one value straight from your API response.

Try

Probability

99.99%

Probability (0–1)

0.99990

Confidence band

Very high

Formulas: p = base^logprob · PPL = base^(−mean logprob).

How it works

A language model doesn't emit a token “confidence” directly — it emits a log probability. Enable logprobs on the OpenAI, Azure OpenAI, vLLM, or llama.cpp APIs and each generated token comes back with a number like -0.0004 or -2.31. These are in natural log (base e), confirmed in the OpenAI API reference. This tool turns them back into numbers you can reason about.

Single probability. The probability of a token is p = e^logprob, and its percentage is p × 100. A logprob of 0 means 100%; a very negative logprob means a probability near 0%. (OpenAI Cookbook, “Using logprobs”.)
Validity guard.A real probability can't exceed 1, so any logprob > 0 is impossible. The tool flags it and clamps the display to 100% instead of showing a nonsense value.
Sequence log-probability. For an N-token output, sum the logprobs: L = Σ logprobᵢ.
Joint probability. The probability of the whole output is P = e^L = ∏ pᵢ — the product of the per-token probabilities, from the chain rule used by autoregressive decoders. Long outputs multiply many sub-1 values, so their joint probability is small by nature.
Average and geometric mean. The mean logprob is L̄ = L / N, and the geometric-mean per-token probability is e^L̄ — a length-independent confidence figure.
Perplexity. PPL = e^(−L̄) = P^(−1/N): the effective number of equally-likely tokens the model was choosing between. 1.0 is perfect certainty; higher means more uncertainty. (Jurafsky & Martin, SLP3, Ch. 3.) The calculator derives it two independent ways and confirms they match.
Top alternatives. When your response includes top_logprobs, each candidate is converted with the same formula and sorted. These are the top-k only, so they don't sum to 100%.

The confidence bands (Very high ≥ 90%, High ≥ 70%, Medium ≥ 40%, Low ≥ 15%, Very low below 15%) are a reading aid layered on top of the exact math — a heuristic to skim a long output, not an official or calibrated metric. The underlying probability and perplexity numbers are the ground truth.

Worked examples

Single token — the −ln 10 identity

Input: logprob = -2.302585 (natural log)
p = e^(-2.302585) = 0.10000
Percentage = 0.10000 × 100 = 10.00%
Band: Very low (below 15%)
Check: -ln(10) = -2.302585, so this must be exactly 10% ✓

Four-token answer — “The capital … Paris.”

Logprobs: [-0.01, -0.22, -1.60, -0.05], threshold 50%
Per-token: 99.00%, 80.25%, 20.19%, 95.12%
Lowest-confidence token = “Paris” at 20.19% (badged, below 50%)
Sum L = -1.88 → joint P = e^(-1.88) = 0.15259 → sequence confidence 15.26%
Mean logprob L̄ = -0.47 → perplexity = e^(0.47) = 1.600
Cross-check: P^(-1/4) = 0.15259^(-0.25) = 1.600 ✓

Edge case — an impossible positive logprob

Input: logprob = 0.5 (a sign mistake, perhaps)
e^(0.5) = 1.6487 → probability 164.87%, which is impossible
The tool clamps the display to 100% and shows a warning
Fix: logprobs are always ≤ 0; re-check the sign of your value

Frequently asked questions

Sources & references

Formulas on this page were last cross-checked against these sources on 2026-07-09. Perplexity is verified two ways (exp(−mean logprob) and P^(−1/N)) inside the calculator.

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