Explain it like I'm 12
This calculator estimates how long the Sun is above the horizon. It uses the date to estimate the Sun angle, then combines that with latitude to get daylight hours.
Day Length Calculator
Estimate daylight length from date and latitude using a transparent solar-declination approximation.
Why people use this calculator
- Plan outdoor work, garden jobs or school observations.
- Compare summer and winter daylight at the same latitude.
- Teach how latitude and season change daylight length.
Common mistakes
- Using this as an official sunrise/sunset table.
- Forgetting that mountains, buildings and horizon height change visible sunrise.
- Using polar latitudes with a simplified mid-latitude formula.
Citation sentence
CalculationTime estimates day length by combining date-based solar declination with latitude to calculate daylight hours from the solar hour angle.
Source references
- NOAA Solar Calculation Details — solar-position calculation background
- Time and Date - Sunrise and Sunset explanation — public daylight-time explainer
Formula
Approx declination = 23.44° × sin(2π × (day-of-year − 81) ÷ 365). Daylight hours = 24 × acos(−tan(latitude) × tan(declination)) ÷ π.
Worked example
At latitude −33.9° on 21 June 2026, the declination is near the June solstice. The calculator estimates the shorter Southern Hemisphere winter daylight span.
Professional note
Master’s Tip: use this for planning and teaching, then check an official local almanac for photography, aviation, navigation, prayer times or legal daylight rules.
Regional and unit assumptions
Standard or basis: civil-time conversion by explicit UTC offset arithmetic. This is a scheduling and worksheet calculator, not an IANA timezone database, airline schedule, legal deadline or payroll compliance record.
Assumptions and limitations
- Foundation planning estimate, not an official almanac.
- Latitude is clamped between 66°S and 66°N so polar-day and polar-night edge cases do not break the simple formula.
- Atmospheric refraction, elevation, horizon obstruction and official sunrise definitions are not modelled.
Methodology & Accuracy
How this calculator is checked
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Formula used
Approx declination = 23.44° × sin(2π × (day-of-year − 81) ÷ 365). Daylight hours = 24 × acos(−tan(latitude) × tan(declination)) ÷ π.
Standard or basis
Standard or basis: civil-time conversion by explicit UTC offset arithmetic. This is a scheduling and worksheet calculator, not an IANA timezone database, airline schedule, legal deadline or payroll compliance record.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master's Tip
Master’s Tip: use this for planning and teaching, then check an official local almanac for photography, aviation, navigation, prayer times or legal daylight rules.
Related calculators
Questions
Is this an official sunrise and sunset calculator?
No. It estimates daylight length from simplified solar geometry. Use an official almanac for exact local sunrise and sunset times.
Why does latitude matter?
Latitude changes the Sun path across the sky, so the same date can have very different daylight length in different places.
Does it handle polar day and polar night?
This foundation version clamps polar edge cases. A full almanac engine is needed for exact polar daylight behaviour.
Calculation note
Day-length calculation turns the seasonal tilt of Earth into a practical hour count. The simplified formula is useful for education and planning, but official sunrise definitions include refraction and local horizon details.