The Sun’s position decides solar panel output, shadows, room lighting and photography’s golden hour. It changes with latitude, season and time of day.
How to use the Sun Angle Calculator
- Latitude (° N positive)
- Longitude (° E positive)
- Date
- Time zone (UTC offset in hours)
- Local time
- Object height (for shadow)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the latitude and longitude, the date, the local clock time and its UTC offset (remember daylight saving time), and an object height for the shadow.
Tips
- These calculators model simple experiments you can try at home.
- Measure each length several times and average the results.
- Small measurement errors can change results noticeably – estimate your uncertainty.
- Everything runs in your browser.
Common mistakes to avoid
- Measuring distances from the wrong reference point.
- Mixing centimetres and metres.
- Ignoring air resistance in fast or light objects.
Inputs explained
| Field | What to enter |
|---|---|
| Latitude (° N positive) | A number |
| Longitude (° E positive) | A number |
| Date | A date |
| Time zone (UTC offset in hours) | A number |
| Local time | A clock time (hours and minutes) |
| Object height (for shadow) | Units: m, cm, mm, km, in, ft … |
What each result means
- Equation of time = 4×(mod([L] – deg(atan2(cos([eps])×sin([lambda]), cos([lambda]))) + 540, 360) – 180)
- Solar declination = deg(asin(sin([eps])×sin([lambda])))
- Hour angle = [tst]÷4 – 180
- Solar elevation = 90 – deg(acos([cz]))
- Solar zenith angle = deg(acos([cz]))
Example values
How the main result changes when Latitude changes and everything else stays at the example values above:
| Latitude (° N positive) | Solar elevation (°) |
|---|---|
| 25.75 | 51.866 |
| 38.63 | 39.046 |
| 51.51 | 26.209 |
| 64.38 | 13.364 |
| 77.26 | 0.516 |
Formula
Solar longitude λ and obliquity ε give declination δ = asin(sin ε·sin λ) and the equation of time, hour angle ha = (true solar time)/4 − 180°cos θ_z = sin φ sin δ + cos φ cos δ cos ha, elevation = 90° − θ_z, shadow = height / tan(elevation)Worked example
Inputs — Latitude (° N positive): 51.5074; Longitude (° E positive): -0.1278; Date: 2026-10-25; Time zone (UTC offset in hours): 0; Local time: 12:00; Object height (for shadow): 1.8 m.
Results — Equation of time = 15.934 min; Solar declination = -12.1954 °; Hour angle = 3.8557 °; Solar elevation = 26.209 °; Solar zenith angle = 63.791 °; Solar azimuth (from north, clockwise) = 184.2 °; Shadow length = 3.6566 m.
Key terms
- Solar azimuth
- Compass direction of the Sun.
Frequently asked questions
Why include the time zone?
Solar position depends on true solar time, not clock time.
What is the equation of time?
The difference between solar time and mean clock time (up to ±16 min).
How accurate is this?
About ±0.1° for current dates, ignoring refraction.
What does a negative elevation mean?
The Sun is below the horizon.
What formula does the Sun Angle Calculator use?
Solar longitude λ and obliquity ε give declination δ = asin(sin ε·sin λ) and the equation of time, hour angle ha = (true solar time)/4 − 180°.