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Apparent Size Calculator | Angular size from object & distance

Find how large an object appears from a distance as an angular size, using the small-angle formula with the working shown. Essential for astronomy, photography framing and any size-versus-distance comparison.

Last updated: June 2026 · Free · No sign-up required

Results

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

ObjectSize / distanceApparent size
Moon3,474 / 384,400 km≈0.52°
Sun1.39M / 149.6M km≈0.53°
2 m door at 100 m2 / 1001.15°
Thumb at arm’s length2 / 60 cm≈2°

info Apparent Size Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

Angular sizePerception
< 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

lightbulb Worked example

Let's say you are using the Apparent Size Calculator. Calculates apparent size using θ = 2 × atan(size ÷ (2 × distance)), instantly in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad

The Apparent Size Calculator is built on a well-established calculation method. It uses the formula θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad to turn your inputs into a reliable result. Calculates apparent size using θ = 2 × atan(size ÷ (2 × distance)), instantly in your browser. The steps are shown on the page so you can follow the reasoning from input to output.

  1. Enter the object’s actual size and its distance in the same units.
  2. The tool computes θ = 2·atan(s÷2d) — exact at any distance, unlike the small-angle shortcut.
  3. 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.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What is apparent (angular) size?
It is how large an object appears from your viewpoint, measured as an angle rather than a length: θ = 2 × atan(size ÷ (2 × distance)). The Moon and the Sun both appear about half a degree wide despite their vastly different sizes, because distance compensates for size. Astronomers use this angle to compare objects that cannot be measured directly.
What is the formula for angular size?
The Apparent Size Calculator uses the standard θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
How big does the Moon appear?
Yes — the Apparent Size Calculator is fully responsive and works in any modern browser on a phone, tablet, or desktop, with touch-sized inputs and no app to install. The full calculation runs on the device, so you get the same speed and precision on mobile as on a computer, even with a weak connection.
What are arcminutes and arcseconds?
The Apparent Size Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates apparent size using θ = 2 × atan(size ÷ (2 × distance)), instantly in your browser. There is no limit on usage, and it works on any device.
Do size and distance need the same units?
Yes — the formula θ = 2 × atan(size ÷ (2 × distance)) requires the object size and its distance in the same unit, because only the ratio matters. The calculator converts automatically if you select different units, and the resulting angle is unit-independent: a 10 m object at 100 m appears the same angular size as a 1 m object at 10 m.
What does the Apparent Size Calculator do?
Calculates apparent size using θ = 2 × atan(size ÷ (2 × distance)), instantly in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Apparent Size Calculator use?
It uses θ = 2 × atan(size ÷ (2 × distance)), and for small angles the approximation θ ≈ size ÷ distance (in radians) is also shown. Enter the object's true size and its distance in matching units, and the tool returns the angular size in degrees or arcminutes, the unit used for stars, planets, and landscape objects.
Is the Apparent Size Calculator free and private?
Yes — the Apparent Size Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Apparent Size Calculator?
The Apparent Size Calculator applies the standard formula: θ = 2 × atan(size ÷ (2 × distance)); small angles: θ ≈ size÷distance rad. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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