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Apparent Size Calculator | Angular size from object & distance

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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

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Results

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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.

From our guides

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: framing a person on camera

A 1.75 m tall person stands 4 m from the camera. Will they fit a lens with a 27° vertical field of view? θ = 2 × atan(1.75 / (2 × 4)) = 2 × atan(0.21875) = 2 × 12.34° ≈ 24.68°.

Result: ≈ 24.7° — fits inside a 27° frame with about 2.3° of margin.

What this means: At 3 m the same person subtends 2 × atan(1.75/6) ≈ 32.5° and gets cropped. Angular size grows fast as distance shrinks, which is why stepping closer changes framing more than photographers expect — the exact 2·atan formula keeps close-range answers honest where the small-angle shortcut drifts.

Formula & methodology

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

How angular size is computed

Apparent size is the angle an object spans in your field of view, from its actual size and distance (both in the same units):

θ = 2 × atan( size / (2 × distance) )

  • For small angles, θ ≈ size / distance in radians is a fine shortcut — this page uses the exact formula so close-range results stay correct.
  • Results are shown in degrees, radians, arcminutes (degrees × 60), and arcseconds (degrees × 3600).

Reading the result

A 1.75 m person at 4 m subtends about 24.7° — compare that with your camera's field of view to see if they fit the frame. The full Moon spans roughly 0.52° (about 31 arcminutes), a handy real-world reference for judging angles.

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.
Will a person fit in my camera's frame?
Compare their angular size to your lens's field of view. A 1.75 m person standing 4 m away subtends θ = 2·atan(1.75/8) ≈ 24.7° vertically. If your lens covers 27° vertically, they just fit with a little margin. Move to 3 m and the angle grows to about 32.5° — now the head or feet get cropped.
How small an angle can the human eye resolve?
About 1 arcminute (1/60 of a degree) under good light — the basis of 20/20 vision. The full Moon spans roughly 31 arcminutes, so it covers about 31 resolution elements across its disc. Astronomers quote telescope and atmospheric limits in arcseconds (1/3600 of a degree) for the same reason.
When does the small-angle approximation break down?
θ ≈ size/distance in radians works well below about 10°, where the error stays under 0.5%. A 2 m door at 100 m subtends 1.15° either way — indistinguishable. But a 10 m object at 10 m is 53.13° exactly versus 57.3° approximated, an error over 4°. This calculator uses the exact 2·atan formula, so close-range results stay correct.
Why do the Sun and Moon look the same size?
A coincidence of ratios: the Sun is about 400 times wider than the Moon but also about 400 times farther away. The Moon (3,474 km at 384,400 km) subtends about 0.518°, and the Sun (1.39 million km at 149.6 million km) about 0.533° — nearly identical, which is why total solar eclipses fit so precisely.

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