Equation of Time Calculator

Calculator Inputs

Date

Used to compute the day of year (N).

Clock Time

Example: 09:30 or 09:30:00.

Model

Choose speed versus comparison detail.

Time Zone Offset (hours)

Use standard offset, like +5 or −4.

Daylight Saving

Applied to the standard meridian only.

Longitude (degrees, East positive)

Range −180 to 180. West is negative.

How to use Formula

How to Use This Calculator

Pick a date and enter a clock time.
Enter your time zone offset and select daylight saving if needed.
Enter longitude in degrees, with east positive and west negative.
Choose a model, then press Calculate.
Read the equation of time, time correction, solar time, and solar noon.
Use Download CSV or Download PDF for records.

Formula Used

Equation of Time (NOAA approximation) gives the offset between apparent and mean solar time:

EoT = 229.18 × (0.000075 + 0.001868 cos γ − 0.032077 sin γ − 0.014615 cos 2γ − 0.040849 sin 2γ)

γ = 2π/365 × (N − 1 + (hour − 12)/24)

Time Correction Factor adjusts clock time using longitude and EoT:

TCF (min) = 4 × (Longitude − LSTM) + EoT

LSTM = 15° × (time zone offset, including DST)

Local Solar Time is then:

Local Solar Time = Clock Time + TCF/60

Solar noon occurs when Local Solar Time equals 12:00.

Example Data Table

Values are typical mid-day estimates and vary slightly by model.

Date	Approx. EoT (min)	Interpretation
February 11	−14:00	Sundial behind clock time
April 15	−0:10	Near zero correction
May 14	+3:40	Sundial ahead of clock time
July 26	+6:30	Moderate positive correction
September 1	−0:20	Near zero correction
November 3	+16:20	Largest positive correction period

Equation of Time Guide

1) What the equation of time represents

The equation of time (EoT) is the difference between apparent solar time and mean solar time. Apparent time comes from the Sun’s real position, while mean time assumes a uniform “average Sun.” The offset is reported in minutes and seconds.

2) Typical yearly range and sign

Across a year, EoT commonly spans about −14 minutes to +16 minutes. Negative values mean the sundial runs behind a clock; positive values mean the sundial runs ahead. The largest positive values often occur in early November, while the most negative values often occur around mid‑February.

3) Why it changes through the year

Two effects dominate: Earth’s axial tilt and Earth’s slightly elliptical orbit. Tilt changes how the Sun’s apparent motion projects onto the equator, and orbital eccentricity changes Earth’s speed along its orbit. Together they create the seasonal EoT curve.

4) Using longitude and the standard meridian

Clocks are set by time zones, not by your exact longitude. Each zone has a standard meridian at 15° × (time zone hours). A location east of that meridian experiences earlier solar time; a location west experiences later solar time. The calculator combines this with EoT.

5) Time correction factor (TCF) in minutes

The time correction factor is computed as 4 × (Longitude − LSTM) + EoT. The “4” converts degrees to minutes because Earth rotates 1° in about 4 minutes. TCF tells you how many minutes to add to clock time to get local solar time.

6) Solar noon shift you can expect

Solar noon is when local solar time equals 12:00. If TCF is +10 minutes at your inputs, solar noon occurs about 10 minutes earlier than 12:00 on your clock; if TCF is −10 minutes, solar noon occurs about 10 minutes later.

7) Practical uses in planning and measurements

EoT improves sundial comparisons, shadow‑length experiments, and any workflow needing accurate solar timing. It helps align observations with true solar noon, supports educational labs, and can refine quick estimates of the Sun’s daily timing when precise ephemeris data is not required.

8) Model choice and accuracy notes

The NOAA-style approximation uses a fractional-year angle and generally matches published EoT tables closely for everyday use. The simple model is faster and illustrative, but it can differ by a minute or more on some days. For best corrections, use the NOAA option.

FAQs

1) Is equation of time the same as daylight saving?

No. Daylight saving is a civil clock change. EoT is a natural offset between apparent and mean solar time caused by Earth’s tilt and orbital shape.

2) What does a positive EoT mean?

Positive EoT means apparent solar time runs ahead of mean time. In simple terms, a sundial would read later than a clock at the same moment.

3) Why do I need longitude if I already know my time zone?

Time zones use a standard meridian, but your longitude may differ. Longitude shifts local solar time by about four minutes per degree from the standard meridian.

4) What longitude sign should I enter?

Use east-positive and west-negative. For example, 74°W is −74, and 67°E is +67. This matches the correction direction used in the calculator.

5) How accurate is the NOAA approximation?

It is typically accurate to within tens of seconds for most practical purposes. Small differences can occur versus high-precision ephemerides, especially if you need sub‑second timing.

6) Can I use this for solar panel tracking?

It can help estimate true solar noon timing and improve quick checks. For detailed tracking control, use full solar position models that include declination and atmospheric refraction.

7) Why do my results change with clock time?

The NOAA model includes a fractional-year term that slightly depends on time-of-day. Around midday the change is small, but entering the correct time gives the most consistent correction.