Day length, sunrise and sunset calculator

How it works

Formula: Day length = 8 × sunrise hour angle (minutes)

The tool follows NOAA's solar calculator, based on Jean Meeus's astronomical algorithms: the sun's position for the date, its declination, the equation of time, then the hour angle of sunrise. Sunrise and sunset are when the sun is 0.833° below the horizon, to account for refraction. According to NOAA, results are accurate to within a minute between 72° north and 72° south.

• NOAA Global Monitoring Laboratory — Solar Calculation Details
• NOAA — NOAA_Solar_Calculations_day spreadsheet

Worked examples

• New York on June 21

  15 h 6 min of daylight.

• Chicago on December 21

  9 h 8 min of daylight.

• At the equator on June 21

  12 h 7 min: close to 12 hours all year.

Common mistakes

• Flipping the sign of the longitude.

  West of Greenwich, longitude is negative: Chicago is at −87.6°.

• Forgetting daylight saving time.

  Pick the place's time zone: the tool applies its daylight saving rules for that date.

• Expecting exactly 12 hours at the equinox.

  Refraction shows the sun a little before it actually rises: the day is a few minutes over 12 hours.

What the calculation leaves out

• According to NOAA, within a minute between 72° N and 72° S, within 10 minutes beyond; the atmosphere can shift what you observe.
• Terrain (mountains, buildings) isn't included: the horizon is assumed flat.

Day length on the 21st of each month at New York (40.7° N)

Frequently asked questions