How we source formulas, verify accuracy, and handle corrections. Updated June 2026.
Geometry Calculator publishes computational tools and educational explanations covering Euclidean, analytic, and solid geometry. Every formula on this site is derived from established mathematical literature — not paraphrased from competing websites and not generated by language models without verification. The numerical output of each calculator is validated against textbook reference solutions before release.
We treat formulas, derivations, and worked examples as primary content. Calculator widgets are wrappers around that content — never substitutes for it. A page describing the Pythagorean theorem must teach the theorem, not merely compute it.
Formulas are drawn from the following primary references, in roughly the order we consult them:
Where a result has a contested or version-dependent statement (for example, the "ambiguous case" in SSA triangles, which has zero, one, or two valid solutions depending on the inputs), we cite the source in the calculator's tutorial and explain the branch logic on-page.
Every calculation runs in your browser using IEEE 754 double-precision floating-point arithmetic. We deliberately use numerically stable formulations even when they are longer than the textbook version — for example, Heron's formula on this site is implemented in its Kahan-stable rearrangement to avoid catastrophic cancellation on nearly-degenerate triangles. The acos and asin calls used in our Law of Sines / Law of Cosines branches are clamped to [-1, 1] before evaluation, so floating-point round-off at the boundaries cannot produce a NaN.
A 22-case automated self-test suite ships with the calculator engine. Every input/output pair in the suite is a textbook-canonical value taken from a primary reference (Heron's formula on a 3-4-5 right triangle, the SSA ambiguous case at a = 6, b = 8, A = 35°, etc.). Each release runs the suite and we do not deploy if any case fails. Administrators can view the suite at ?gc_calc_self_test=1.
The "AI Solve" button on each calculator sends your inputs to a large language model (currently a mix of Anthropic Claude, OpenAI GPT, and DeepSeek depending on the problem type — see Methodology for the full routing table). The model receives the same inputs you typed plus a system prompt that instructs it to explain the solution step-by-step and to follow the formulas we use in the calculator.
AI explanations are reviewed in spot-checks but are not verified case-by-case against an authoritative solution. We treat AI Solve output as a teaching aid, not as a definitive answer. The numeric result shown above the explanation is computed deterministically by our calculator engine, not by the LLM, and is the authoritative answer. If the AI explanation appears to reach a different number, trust the calculator's number and email us so we can investigate the prompt.
When we find an error — whether by self-test failure, user report, or routine review — we issue a correction the same day. Significant corrections are logged in the site's changelog (visible via the version number in the admin footer) and the affected page's "Last updated" date is bumped. Cosmetic edits (typos, formatting) do not bump the date.
If you find a numeric or formula error, please email us with the calculator slug, the inputs you used, the value you got, and what you believe the correct value should be (with a source if possible). We aim to acknowledge within 48 hours and resolve within one week.
Geometry Calculator is a teaching and computation tool. It is not a substitute for professional engineering, architectural, surveying, or construction calculations. Critical structural, navigational, or safety calculations should always be performed by a licensed professional and cross-validated against multiple independent sources. See our Disclaimer for the full scope and limitation statement.