Great3 Grid C alpha set 06 (minor 0.14, major 0.32)

Solid Angle Visualizer

How to use this tool

Orbit / Move: Drag background to orbit. Drag the blue patch center to move (θ, φ).
Bounds: Drag θ₁ and θ₂ (yellow) / φ₁ and φ₂ (purple) to set integration limits.
Use controls for exact numbers; Preset/Reset to compare cases.

Small demo

Grid Guides

Mode:

Ω: — sr

Ω = — sr

Centerθ₁/θ₂φ₁/φ₂

Radius: [ ] arb

Sandbox: freely drag the patch center and the θ/φ bounds.

Try: change θ₁/θ₂ vs change φ₁/φ₂ (Δφ) and watch Ω respond.

Key insight: Ω is unit-sphere area (direction space), not a planar angle.

x

z

Interactive

Small demo

Drag the patch center and the θ/φ bounds to build intuition about solid angle Ω.

Tip: choose another preset to view a locked teaching demo.

→ θ, φ

● dθ

● dφ

→ φ

Ω = — sr

x

z

Preset

FOV

Parameters

controls

Adjust parameters. Readout stays visible on the right.

Angle mode

Degrees

Radians

Mode: Degrees (°)

rad = deg×(π/180) | deg = rad×(180/π)

θ bounds

theta

Theta upper (θ₁)deg

Theta lower (θ₂)deg

—

Φ bounds

phi

Phi start φ₁ deg

Phi end φ₂ deg

—

For educational purposes only. Not intended for high-precision engineering.

Live Readout

numbers

Updates instantly as you drag or change sliders.

Solid angle

Ω = —

sr

Spherical area

dA = —

arb²

Note: Values shown are rounded for readability (fixed: up to 4 decimals; very small/large values use scientific notation with ~5 significant digits). Calculations use full precision, so tiny values may look “short” but the results are accurate.

1 θ bounds & φ bounds

—

2 Convert Δφ to radians

—

3Integrate over θ

∫ sinθ dθ: —

This term depends only on θ₁ and θ₂.

4Compute Ω

Ω = Δφ · (cosθ₁ − cosθ₂)

—

If you change any bound (θ₁/θ₂/φ₁/φ₂), Ω updates instantly.

One-look summary

Solid angle Ω is the unit‑sphere area of a direction region. Spherical area on radius r is dA = r²·Ω.