Best AI model to solve reasoning and math problems
Problems that take several reasoning steps, such as math, logic and calculation. Models usually think a lot before answering here, which uses output tokens.
Suggested models
1 Claude Fable 5.2 Anthropic
Why it fits: Gets 95.1% on FrontierMath (tiers 1 to 3), research level math problems kept secret, so the model cannot have memorized them.
- FrontierMath (tiers 1 to 3): 95.1%, per Epoch AI, latest version we checked?what it is
- Price: US$ 8.00 input and US$ 40.00 output per 1M tokens (source: Anthropic, official page)?
- Estimated cost (see the How we calculate block): about US$ 0.32 (estimate)
- Weights: Closed?
- Alternative: Kimi K3.1 Pro, with open weights, 78.2% on FrontierMath (tiers 1 to 3)
2 GPT-6.1 Sol OpenAI
Why it fits: Gets 93.7% on FrontierMath (tiers 1 to 3), research level math problems kept secret, so the model cannot have memorized them.
- FrontierMath (tiers 1 to 3): 93.7%, per Epoch AI, latest version we checked?
- Price: US$ 2.00 input and US$ 10.00 output per 1M tokens (source: OpenAI, official page)?
- Estimated cost (see the How we calculate block): about US$ 0.081 (estimate)
- Weights: Closed?
- Alternative: Kimi K3.1 Pro, with open weights, 78.2% on FrontierMath (tiers 1 to 3)
3 GPT-6 Astra OpenAI
Why it fits: Gets 93.7% on FrontierMath (tiers 1 to 3), research level math problems kept secret, so the model cannot have memorized them.
- FrontierMath (tiers 1 to 3): 93.7%, per Epoch AI, latest version we checked?
- Price: US$ 10.00 input and US$ 50.00 output per 1M tokens (source: OpenAI, official page)?
- Estimated cost (see the How we calculate block): about US$ 0.40 (estimate)
- Weights: Closed?
- Alternative: Kimi K3.1 Pro, with open weights, 78.2% on FrontierMath (tiers 1 to 3)
4 Claude Opus 5.5 Anthropic
Why it fits: Gets 91.2% on FrontierMath (tiers 1 to 3), research level math problems kept secret, so the model cannot have memorized them.
- FrontierMath (tiers 1 to 3): 91.2%, per Epoch AI, latest version we checked?
- Price: US$ 4.00 input and US$ 20.00 output per 1M tokens (source: Anthropic, official page)?
- Estimated cost (see the How we calculate block): about US$ 0.16 (estimate)
- Weights: Closed?
- Alternative: Kimi K3.1 Pro, with open weights, 78.2% on FrontierMath (tiers 1 to 3)
Order: highest FrontierMath (tiers 1 to 3) score among reasoning and math models, one version per model line.
How we calculate
Change the numbers and the cost of every model on the page is recalculated right away. Without JavaScript, the default values below apply.
Input = words in the problem ÷ 0.75. Output = reasoning and answer tokens, which vary a lot between models.
With these numbers: about 400 input tokens and 8,000 output tokens (estimate).
Conversion used: 1 token is about 4 characters or 0.75 words, OpenAI's rough rule for English text. Other languages can differ. Conversion source: OpenAI, Understanding and counting tokens
Fields marked as assumption are our own guesses, without a source. Adjust them to your case.
Cost of each model = input tokens × input price + output tokens × output price, with prices per 1M tokens. Models that reason before answering can use many more output tokens. It is a reference calculation and does not change the order of the list.
Other paid models we checked
Reference paid models from the main labs. They are left out of the list above because of a lower score, no score on this metric, or not passing the case filter. Prices come from the company's official page when it publishes them.
| Model | Score on this metric | Price and source | Estimated cost |
|---|---|---|---|
| GPT-6 Luna OpenAI | 78.9% | US$ 0.10 input and US$ 0.50 output per 1M tokens (source: OpenAI, official page) | about US$ 0.004 (estimate) |
| Claude Sonnet 5.5 Anthropic | 88.8% | US$ 2.00 input and US$ 10.00 output per 1M tokens (source: Anthropic, official page) | about US$ 0.081 (estimate) |
| Claude Haiku 5.5 Anthropic | 75.1% | US$ 0.10 input and US$ 0.50 output per 1M tokens (source: Anthropic, official page; up to 100,000 prompt tokens) | about US$ 0.004 (estimate) |
| Gemini 4 Argon Google | 86% | US$ 2.00 input and US$ 10.00 output per 1M tokens promotional price (source: Google, official page; promotional price currently shown on the page; Google has said this price will go up) | about US$ 0.081 (estimate) |
| Gemini 3.8 Flash Google | 68.4% | US$ 0.75 input and US$ 3.75 output per 1M tokens promotional price (source: Google, official page; promotional price currently shown on the page; Google has said this price will go up) | about US$ 0.03 (estimate) |
| Grok 4.7 xAI | 53% | US$ 2.00 input and US$ 6.00 output per 1M tokens (source: xAI, official page) | about US$ 0.049 (estimate) |
| Mistral Large 4 Mistral AI | 58.6% | US$ 0.50 input and US$ 1.50 output per 1M tokens (source: Mistral AI, official page; price the official page gives for Mistral Large, without naming the version) | about US$ 0.012 (estimate) |
| Mistral Medium 3.5 Mistral AI | no score on this metric | US$ 1.50 input and US$ 7.50 output per 1M tokens (source: OpenRouter; the price could not be read from the official page, because the table is built automatically; OpenRouter is kept as the reference) | about US$ 0.061 (estimate) |
| Command A Cohere | no score on this metric | US$ 2.50 input and US$ 10.00 output per 1M tokens (source: OpenRouter; Cohere's official page does not publish this model's price; OpenRouter is kept as reference) | about US$ 0.081 (estimate) |
| Command A+ Cohere | no score on this metric | US$ 0.30 input and US$ 1.50 output per 1M tokens (source: OpenRouter; Cohere's official page does not publish this model's price; OpenRouter is kept as reference) | about US$ 0.012 (estimate) |
| Nova Premier 1.0 Amazon | no score on this metric | US$ 2.50 input and US$ 12.50 output per 1M tokens (source: Amazon, official page; us-east-1 region, official AWS price list) | about US$ 0.10 (estimate) |
| Nova 2 Lite Amazon | no score on this metric | US$ 0.33 input and US$ 2.75 output per 1M tokens (source: Amazon, official page; us-east-1 region, official AWS price list) | about US$ 0.022 (estimate) |
FAQ
What is the best AI model to solve reasoning and math problems?
By this page's rule, the list starts with Claude Fable 5.2, GPT-6.1 Sol, GPT-6 Astra, Claude Opus 5.5. Order: highest FrontierMath (tiers 1 to 3) score among reasoning and math models, one version per model line.
How much does it cost to solve reasoning and math problems with AI?
With the default values in the How we calculate block, the estimate ranges from US$ 0.081 to US$ 0.40 among the listed models with a published price. It is only an estimate and you can adjust the numbers on the page.
Is there an open weights option to solve reasoning and math problems?
Not among the models on this list. In the catalog sources, no open weights model has a score for this case.
Does this page use AI to recommend?
No. The recommendation comes from fixed rules over public data from Epoch AI, OpenRouter, Hugging Face and each company's official pricing page, in the latest version we checked. The typed text is only compared with keywords.
Terms used on this page
Use cases with their own page
Official pricing pages checked
Sources
- Epoch AI, CC BY 4.0, latest version we checked.
- OpenRouter Benchmarks, CC BY 4.0, latest version we checked.
- OpenRouter, dados públicos da API; exports de benchmarks e rankings em CC BY 4.0, latest version we checked.
- Hugging Face Hub, metadados públicos do Hub; licença de cada modelo no repositório, latest version we checked.
Dates come from the sources: OpenRouter listing or Hugging Face repo creation, which may differ from the official launch. Family and version were grouped by rule from the name.