doomath Calculator
Sun & Solar Angles Calculator
Calculate sun position, solar elevation angle, azimuth, solar noon, golden hour times and shadow length for any latitude and day.
InputsChange a value to recalculate instantly
ResultUpdates as you type
PHYSICAL SIMULATOR
Solar Elevation & Daylight Simulator
LIVE ENGINE 60FPS
Solar Position & Daylight Arc
Interactive simulation of solar elevation angle, twilight transition, and daylight hours.
Solar Noon Zenith Arc Active
FORMULA & STEPSSun & Solar Angles Calculator — Mathematical Derivation & Steps
3 StepsSequential Calculation Breakdown
1
Solar Declination Angle (δ)
The tilt of Earth axial orientation relative to the Sun on day 172.
2
Solar Elevation Angle (α)
The Sun is currently above the horizon.
3
Shadow Projection Length
Shadow cast by a 1.8m vertical object onto flat terrain.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Sun & Solar Angles Calculator
Calculate sun position, solar elevation angle, azimuth, solar noon, golden hour times and shadow length for any latitude and day.
01Set inputsChoose values, units and assumptions.
02Apply the modelSolar Elevation: sin(α) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H); Shadow: L = h ÷ tan(α)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Enter observer latitude, day of the year, and local solar hour. The model calculates solar declination, elevation angle, azimuth, and ground shadow projection length.
Formula & method
Solar Elevation: sin(α) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H); Shadow: L = h ÷ tan(α)
Assumptions & notes
- Declination varies from -23.44° to +23.44° throughout the year.
- Golden hour occurs when solar elevation is between -4° and +6° above horizon.
- Atmospheric refraction subtly elevates apparent solar position near the horizon.