01 · Where the sun is
Mean longitude, mean anomaly and the equation of center give the apparent longitude ; with the obliquity that fixes declination and right ascension — the Astronomical Almanac’s low-precision solar series, good to ~0.01°.
Playground · research instrument
Sun Path Calculator
How much sun does that spot actually get? Sunrise, solar noon, sunset and golden hour to the minute; how long a shadow anything casts, and which way it points; how many hours of direct sun a garden gets once trees and buildings are in the way; and what a solar array on that roof would make in a day. Any place, any date, worked out in your browser — the astronomy is the same series that draws our globe's day/night terminator.
Independent research instrument — not claimed as MakerPortal shipped product code. Methods, equations, assumptions, and limitations are disclosed so you can inspect what the page does and does not establish.
The answer
The sun is up 13h 23m today — 6:16 AM to 7:39 PM, highest at 12:58 PM, 60° above the horizon.
With an open sky this spot gets 13h 14m of direct sun: full sun.
Inputs
Everything runs in your browser — no location is sent anywhere.
Your browser will ask next. The coordinates are rounded to about a kilometre, used only to solve the sun, and never leave this page — there is no server to send them to.
Sunrise convention: the sun’s center at −0.833° — refraction plus the solar semidiameter at a flat horizon. Solver: the Astronomical Almanac low-precision solar series, the same one drawing the terminator on the live globe.
Sky dome · looking up (east mirrored left)
Sun path for the day
2026-08-25 · faint arcs = June / December solstices
Ground plan · north up, east right
Shadow compass
—
10:00
Solved day
- Sunrise
- 6:16 AM
- Solar noon
- 12:58 PM
- Sunset
- 7:39 PM
- Day length
- 13h 23m
- Sun az / el
- 114.7° · 40.6°
- Shadow (h = 1.8 m)
- 2.10 m
Shadow ratio 1.16 × height · civil dawn/dusk and golden hour solved live
What that much sun is actually worth
Solar panel output — watts, kWh and the best angle
Everything above is geometry: where the sun is. This turns it into energy — how many watts an array of a given size and angle collects through the day, how many kilowatt-hours that adds up to, and the one fixed angle that collects the most over a whole year at this latitude. Clear sky only:no cloud, no terrain, no shading, so read every number as the ceiling a real installation works down from. The best annual angle is steeper than the best summer angle — it buys winter back at the cost of a little June, so switching to it can lower today's figure while raising the year's.
Your array
Where these numbers come from: clear-sky irradiance by Bird & Hulstrom (1981), turned onto your panel angle by the HDKR sky model, then through the two things that happen at the module itself — Fresnel reflection off the glass (ASHRAE incidence-angle modifier) and the power a silicon cell loses as it heats up (NOCT model, −0.4%/°C). Heat is the bigger one: it costs about 5% a year in London and 12% in Phoenix, which is why it is a modelled term here and not a fudge inside the loss percentage. Checked against the Copernicus clear-sky product (8% mean absolute above 40° sun elevation) and against PVGIS's own annual temperature loss (r = 0.99 across four climates). The system-loss box is the one input here that is a convention rather than physics.
Clear-sky output through the day
Power curve
solid = your angle · dashed = best ANNUAL angle
- Peak output
- 4.76 kW
- Energy today
- 36.2 kWh
- Onto the array
- 7.84 kWh/m²
- At the set time
- 3.40 kW
- Best angle here
- 38° · 180°
- Best vs yours
- +0.8% / yr
on the panel 724 W/m² · beam 838 W/m² · horizontal 650 W/m² · air mass 1.53 · cell 43 °C · glass −2.5% · heat −8.2% · peak at 1:00 PM
What the calculator solves
02 · Over your head
Elevation comes from your latitude , the sun’s declination and the longitude gap . Azimuth is the sun vector against your local east/north/up basis — no hour-angle sign conventions to trip on.
03 · When it crosses
Sunrise, sunset, civil twilight and golden hour are all the same problem: find when elevation crosses a threshold. The solver scans the local day and bisects each crossing to sub-second — so polar day and night fall out as “no crossing”, not an error.
04 · Shadow on the ground
Shadow length for an object of height , pointing away from the sun’s azimuth. The shadow ratio is the site-independent version: 1 at 45° elevation, 5.7 at 10°.
Model boundary. Flat-horizon geometry: no terrain, trees or buildings, which near dawn and dusk dominate real shadows. Event times should match NOAA-class calculators within about a minute; positions to ~0.01°. The horizon is the standard −0.833° (refraction + semidiameter), and times render in the timezone you pick — the astronomy underneath is UTC-exact.
Sun and shadow questions
Why does my sunrise time differ by a minute or two from a weather app?
Sunrise here uses the standard −0.833° horizon: the sun’s upper limb touching a flat sea-level horizon with standard atmospheric refraction. Apps that know your elevation or model terrain can shift the time by a minute or two; so can your actual horizon, by much more. The geometry is the easy part — your hills are the real answer.
What is the shadow ratio?
Shadow ratio is shadow length per unit of object height: 1 / tan(sun elevation). At 45° elevation the ratio is 1 (a 6 ft pole casts a 6 ft shadow). At 10° elevation it is 5.7 — winter-morning shadows run several times the height of the object casting them.
Why is solar noon not at 12:00?
Two reasons stacked: your longitude is usually offset from the center of your time zone (15° of longitude = a full hour), and the equation of time — the difference between a sundial and clock time caused by Earth’s tilted axis and elliptical orbit — swings between about −14 and +16 minutes across the year.
What happens above the Arctic Circle?
The solver reports the truth: on midsummer days the sun never dips below the horizon (no sunrise crossing — polar day) and in winter it never rises (polar night). The sun-path arc simply stays inside or outside the horizon ring, and the day length card says which.
Can I use this for solar panels or a garden?
For geometry, yes: azimuth, elevation, shadow length and direction are exact for a flat horizon. Siting decisions should add your real horizon (trees, buildings, terrain) and local weather — this calculator supplies the sky, not the obstacles.
Shareable still
The instrument, captured—not illustrated.
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