# Julian Date Calculator

> Converts a Gregorian calendar date and time (in UTC or an IANA zone) to the astronomical Julian Day Number, Julian Date (JD), Modified Julian Date (MJD), Truncated Julian Date, days since the J2000.0 epoch and Julian centuries, plus day of year and ISO week.

- Calculator id: `julian-date` · Category: Time & Geography (`time`) · Tool name: `convert_julian_date`
- Canonical page: https://tttkmbb.com/time/julian-date · This document: https://tttkmbb.com/time/julian-date.md · JSON definition: https://tttkmbb.com/time/julian-date.json

## Purpose

Converts a Gregorian calendar date and time (in UTC or an IANA zone) to the astronomical Julian Day Number, Julian Date (JD), Modified Julian Date (MJD), Truncated Julian Date, days since the J2000.0 epoch and Julian centuries, plus day of year and ISO week.

**Use when:** You need JD/MJD values for astronomy, satellite or ephemeris work, or want to know the day count between dates via Julian Day Numbers.

**Do not use when:** You mean the 'Julian date' used in food packaging or the military (a day-of-year number such as 2026-266; see day-of-week for day of year) or Unix epoch seconds (use unix-timestamp).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `date` | date |  | optional, default "today" | Gregorian calendar date (YYYY-MM-DD); defaults to the current UTC date. |
| `time` | string |  | optional, default "00:00" | Time of day, 24-hour HH:MM (seconds optional), in time_zone. |
| `time_zone` | string |  | optional, default "UTC" | IANA zone of the given date and time; JD is always expressed in Universal Time. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `julian_day_number` | integer |  | Integer day count of the UTC calendar date (the JD at 12:00 UT that day); JDN 0 = 1 January 4713 BC (Julian). |
| `julian_date` | number | days | Days since noon UT on 1 January 4713 BC, with the fraction of the day since noon. |
| `modified_julian_date` | number | days | JD − 2,400,000.5 (starts at midnight UT on 17 November 1858). |
| `truncated_julian_date` | integer |  | ⌊JD − 2,440,000.5⌋, NASA convention counting from 24 May 1968. |
| `days_since_j2000` | number | days | JD − 2,451,545.0 (J2000.0 = 2000-01-01 12:00 TT, taken here as UT). |
| `julian_century` | number |  | (JD − 2,451,545) / 36,525, the T used in astronomical formulas. |
| `utc_datetime` | string |  | The instant in UTC (ISO 8601). |
| `day_of_week` | string |  | Day of the week of the UTC date. |
| `day_of_year` | integer |  | Ordinal day of the UTC date, 1 January = 1. |
| `iso_week_date` | string |  | UTC date in ISO 8601 week notation YYYY-Www-D. |

## Formula

`a = ⌊(14 − month)/12⌋, y = year + 4800 − a, m = month + 12a − 3; JDN = day + ⌊(153m + 2)/5⌋ + 365y + ⌊y/4⌋ − ⌊y/100⌋ + ⌊y/400⌋ − 32045; JD = JDN − 0.5 + (hours_UT / 24); MJD = JD − 2400000.5`

Proleptic Gregorian calendar; times are converted to UT via the tz database before the day fraction is added. Leap seconds and the ~69 s difference between UT and Terrestrial Time are ignored (relevant only for sub-minute ephemeris work).

## Data Sources

- USNO Astronomical Applications – Julian Date Converter — https://aa.usno.navy.mil/data/JulianDate (government, retrieved 2026-09-24)
- Julian day – JDN algorithms and epochs (Wikipedia) — https://en.wikipedia.org/wiki/Julian_day (reference, retrieved 2026-09-24)

Data freshness: `daily` (max_age_seconds 86400). Depends on the current date unless the date is supplied.

## API

- `GET https://tttkmbb.com/api/v1/calculate/julian-date?`
- `POST https://tttkmbb.com/api/v1/calculate/julian-date` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/julian-date · OpenAPI operationId `convert_julian_date` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "julian-date", "inputs": {…}}`

## Example

- J2000.0 epoch: 2000-01-01 12:00 UTC: inputs `{"date":"2000-01-01","time":"12:00","time_zone":"UTC"}` → `{"julian_day_number":2451545,"julian_date":2451545,"modified_julian_date":51544.5,"truncated_julian_date":11544,"days_since_j2000":0,"julian_century":0,"day_of_week":"Saturday","day_of_year":1,"iso_week_date":"1999-W52-6"}`
- MJD epoch: 1858-11-17 00:00 UTC: inputs `{"date":"1858-11-17","time":"00:00"}` → `{"julian_date":2400000.5,"modified_julian_date":0,"julian_day_number":2400001,"day_of_week":"Wednesday"}`

```
GET https://tttkmbb.com/api/v1/calculate/julian-date?date=2000-01-01&time=12%3A00&time_zone=UTC
```

## Limitations

You mean the 'Julian date' used in food packaging or the military (a day-of-year number such as 2026-266; see day-of-week for day of year) or Unix epoch seconds (use unix-timestamp). Proleptic Gregorian calendar; times are converted to UT via the tz database before the day fraction is added. Leap seconds and the ~69 s difference between UT and Terrestrial Time are ignored (relevant only for sub-minute ephemeris work). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why does the Julian Date have a .5 at midnight?**

Julian days begin at noon UT, so midnight falls halfway through a Julian day: 2000-01-01 00:00 UT is JD 2451544.5 and 12:00 UT is JD 2451545.0. MJD shifts the origin to midnight to avoid this.

**Is the Julian Date related to the Julian calendar?**

Only historically; the count was proposed by Joseph Scaliger in 1583 and named after his father Julius. The calendar date entered here is Gregorian.

## Related

- [Unix Timestamp Converter](https://tttkmbb.com/time/unix-timestamp.md) — Unix epoch value of the same instant.
- [Day of the Week Calculator](https://tttkmbb.com/everyday/day-of-week.md) — Weekday and ordinal day of year of a date.
- [Date Difference Calculator](https://tttkmbb.com/everyday/date-difference.md) — Days between two dates (equal to the JDN difference).