Tools
Calculators for working through the classroom packets, and for checking the answers afterward. Every tool shows its formula, so a result can be traced back to its working rather than taken on trust.
Graphing calculator
Up to ten functions with live sliders. Finds zeros, turning points and intersections; draws tangent lines and shades areas; builds tables; fits six kinds of regression to your data; switches either axis to a log scale. Includes a scientific calculator and a shareable link for every graph.
Open the calculatorUnit converter
Eleven kinds of quantity, nanometres to megaparsecs and grams to solar masses, in decimal and scientific notation side by side.
Good for: dimensional analysis in every packetWavelength & frequency
λ = v/f in both directions, inside materials as well as vacuum, with half- and quarter-wave lengths and a band calculator for antenna design.
Good for: waves, radio, antennas, spectraAstronomy calculators
Distance modulus, angular size, true 3-D separation, surface brightness, dynamical mass from star speeds, and Kepler's third law.
Good for: galaxies, clusters, dark matterSig figs & error bars
Count and round significant figures, push uncertainty through any formula, and test whether a conclusion survives the error bar.
Good for: precision, measurement, lab reportsConfusion matrix
Accuracy, recall, precision, F1, sensitivity and specificity from one table, then the step most audits skip: how often a mistake actually happens.
Good for: AI, medical tests, statisticsTriangle solver
Any three parts in, everything out: law of sines, law of cosines, the ambiguous two-triangle case, area and a to-scale drawing.
Good for: geometry, trigonometry, surveyingFor teachers
Checking a key. Each tool prints the formula it used and keeps more digits than a worksheet needs, so you can see whether a student's answer differs by rounding or by method.
Projecting a graph. Build a graph, press Copy link, and paste the link into your slides or class page. It reopens with the same functions, sliders and window.
Privacy. Everything runs in the browser. There are no accounts, no tracking of what students type, and nothing is saved on a server.
Tests. These are learning tools. Follow your school's and exam board's rules on which calculators are allowed during assessments.
Constants & conversions
The values the tools use. “Exact” means fixed by definition, not measured.
| Quantity | Value | Note |
|---|---|---|
| Speed of light, c | 299,792,458 m/s | exact; packets usually round to 3.00 × 10⁸ |
| Gravitational constant, G | 6.674 30 × 10⁻¹¹ N·m²/kg² | CODATA; also 4.300 92 × 10⁻³ pc·(km/s)²/M☉ |
| Planck constant, h | 6.626 070 15 × 10⁻³⁴ J·s | exact |
| Electronvolt | 1.602 176 634 × 10⁻¹⁹ J | exact |
| Astronomical unit, AU | 1.495 978 707 × 10¹¹ m | exact |
| Light-year, ly | 9.460 730 × 10¹⁵ m | = 63,241 AU |
| Parsec, pc | 3.085 678 × 10¹⁶ m | = 206,265 AU = 3.2616 ly |
| Solar mass, M☉ | 1.988 × 10³⁰ kg | measured |
| Sun's absolute V magnitude | 4.83 | common textbook value |
| Earth's mean radius | 6,371 km | measured |
| Standard gravity, g | 9.806 65 m/s² | exact, by convention |
| One radian | 206,264.8″ = 57.2958° | exact (180/π degrees) |
| Julian year | 31,557,600 s | exactly 365.25 days |
| Inch · pound | 2.54 cm · 0.453 592 37 kg | exact |
Trusted free resources
Outside sites that are free to use and worth bookmarking. None of them are affiliated with this site.
A full college astronomy textbook, free online and as a PDF. The natural next step after the packets.
Free algebra-based physics text: waves, optics, gravitation and the rest.
Free statistics text covering two-way tables, conditional probability and regression.
University of Colorado's free science and math simulations: waves, orbits, circuits and more.
Browser-based 3-D views of the solar system, missions and exoplanets, from NASA.
Positions and distances of planets, moons, asteroids and spacecraft, from NASA's Jet Propulsion Laboratory.
Real measured data on thousands of confirmed planets: a ready-made data set for regression practice.
Searchable NASA images and video. NASA material is generally not copyrighted; check each item's credit line.
A planetarium in the browser: tonight's sky from anywhere, with no download.
The official CODATA values, if you need more digits than the table above.
Where astronomers post research before (and after) journal review. The source for most packets.
Search engine for published astronomy and physics papers, with free links to most full texts.
The NGSS performance expectations the packets cite.
The official CCSS math standards, including the modeling and quantity standards the packets lead with.
Built to be used with these tools
Each Cosmic Sanctuary packet is a 90-minute case study built on research published this year, with a full worked answer key. The calculators here are free for anyone; the packets are on Teachers Pay Teachers.
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