Sunrise Sunset Times

The Sunrise Sunset Times computes Sunrise (hours) from 2 inputs: latitude, day of year (1-365). Sunrise and sunset by location.

Time calculations span everything from calculating how much a freelancer bills for a multi-timezone project to estimating how old someone will be on a specific future date. The math is simple but the edge cases (leap years, DST, month lengths) trip people up. The Sunrise Sunset Times sits in that toolkit — it sunrise and sunset by location. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

Where

lat

Latitude

doy

Day of year (1-365)

Sunrise (hours)

Output value

Sunset (hours)

Output value

1. 01Start by noting the input — Latitude: 40.
2. 02Start by noting the input — Day of year (1-365): 172.
3. 03Substitute these values into the formula: Sunrise (hours) = 12-180 × acos(-tan(t × π / 180) × tan(n × π / 180)) / π / 15 | Sunset (hours) = 12+180 × acos(-tan(t × π / 180) × ta…
4. 04Compute Sunrise (hours): the calculator returns 4.57774.
5. 05Compute Sunset (hours): the calculator returns 19.4223.
6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.