Apparent Size Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Inside the Apparent Size Calculator
Every result on this page comes from a real formula — θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad — computed live in your browser the moment you press the button.
If you are new to apparent size calculator, start with the worked example in the methodology section below — it walks the formula end-to-end with real numbers — then use the quick-reference table for common scenarios.
Quick reference
| Object | Size / distance | Apparent size |
|---|---|---|
| Moon | 3,474 / 384,400 km | ≈0.52° |
| Sun | 1.39M / 149.6M km | ≈0.53° |
| 2 m door at 100 m | 2 / 100 | 1.15° |
| Thumb at arm’s length | 2 / 60 cm | ≈2° |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
| Angular size | Perception |
|---|---|
| < 1′ (arcminute) | Below naked-eye resolution |
| 1′–30′ | Visible as a point or small disc |
| ≈0.5° | Moon/Sun size — covered by a little fingertip at arm’s length |
| > 20° | Fills a large part of your view |
Formula & methodology
Formula: θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad
- Enter the object’s actual size and its distance in the same units.
- The tool computes θ = 2·atan(s÷2d) — exact at any distance, unlike the small-angle shortcut.
- Results are shown in degrees, radians, arcminutes (×60) and arcseconds (×3600).
Example: a 2 m door at 100 m subtends 1.1458° ≈ 68.7 arcminutes — about twice the full Moon.