Star Trek Stardate + Warp Visualizer

two focused calculators: stardate conversion and warp speed travel estimation

Starting values — Star Trek Stardate + Warp Visualizer

Tool type	warp speed
Era	TNG (2364+)

Change any control above and the results recompute from these.

Loading interactive simulation...

how fast is the Millennium Falcon, really? 🖖

Comparing sci-fi ships means picking one common yardstick, and speed relative to light is the only one that survives crossing franchises — 'warp 9.6' and '2,000c' both cash out to a multiple of 299,792 km/s. The TNG warp scale isn't linear either: v = w^(10/3)·c up to warp 9, then the curve gets divided by (10−w) above that, so speed diverges toward infinity as w approaches 10 — which is why canon treats warp 10 as an unreachable asymptote, not just 'one more notch.' That's why nudging from warp 9.6 (Enterprise-D's rated max) up to warp 9.975 (Voyager's) is roughly an 18× jump in real speed for a change of only 0.375 in the warp number.

one stardate is not a fixed length of time 🖖

In TNG mode the console cuts each calendar year into exactly 1000 stardates, so the unit breathes with the calendar: 8 h 45.6 min in a common year, 8 h 47.0 min in a leap year. That 1.4-minute difference, times the thousand stardates in a year, is precisely the leap day spread thin. TOS mode divides a fixed 365.25-day year instead, so its stardate never changes length — New Year drifts instead. Ask for stardate 43989.1 and then 43990.1 and the console hands back a gap of 8.76 hours, because 2366 happens to be a common year.

the stardate was invented to be random 🖖

In the original 1967 Star Trek Guide, Gene Roddenberry told scriptwriters to invent each episode's stardate by picking any four digits and a decimal — 1313.5, for instance — and to keep it consistent only within a single script, never between episodes. The in-universe excuse was that a stardate depends on a ship's speed and galactic position, so relativity lets it drift. The franchise's most scientific-sounding timestamp was, from the start, a deliberate continuity dodge.

Problems solved in full

The speed of warp factor 6.00 on the TNG asymptotic model 5 steps
Turn a warp factor into a speed you can picture, then find out what the last stretch below warp 10 costs. The console is on the TNG asymptotic model at warp factor 6.00, and it prints its own law beside the readout.
1. The law comes in two branches joined at warp 9. Warp 6 sits below the join, so the denominator never appears and the whole thing is one power.
  
  $v (w) = ⎩ ⎨ ⎧ w^{10/3} c \frac{w ^{10/3}}{10 - w} c w \leq 9 w > 9$
2. 10/3 is 3 + 1/3, so that power splits into a cube and a cube root. Both are within reach by hand once you notice that 1.82 cubed is a shade over 6.
  
  $w = 6.00 \leq 9 ⟹ v = 6^{10/3} c = 6^{3} \cdot 6^{1/3} c$
3. Multiply the pieces back together. The readout drops the decimals, so 392.498 becomes the SPEED line.
  
  $216 \times 1.81712 = 392.498 ⟹ v = 392 c$
4. Multiply by the speed of light in km/s. Nothing new is being computed here — the same speed is simply being said in a unit that has a size.
  
  $v = 392.498 \times 299 792.458 = 1.177 \times 1 0^{8} km/s$
5. A light-year is what light covers in a year, so a ship at 392.498 c covers 392.498 light-years per year by definition, with no relativity involved. Divide by the length of a Julian year for the LY/DAY line.
  
  $\frac{392.498 ly/yr}{365.25 d/yr} = 1.0746 ly/d$
Answer

392 c, which is 1.0746 light-years a day. Cross warp 9 and a denominator appears, and it takes over completely. At warp 9.9 the gap to 10 is 0.1 and the speed is 20,835 c; at 9.95 it is 42,375 c; at 9.975, 85,461 c. Each of those halves the gap and roughly doubles the speed, because the numerator hardly moves over that stretch — it goes from 1,516 at warp 9 to 2,147 at warp 9.99 — while 1/(10 - w) climbs from 1 to 100. So warp 10 is not a very fast setting that the scale never quite reaches. It is a division by zero, and the control stops at 9.99 for the same reason the function does. Read it the other way and the gap becomes the design parameter: a million times light speed needs 10 - w = 0.00214, which is warp 9.99786 — a number the slider cannot even express.

$w \to 1 0^{-} lim \frac{w ^{10/3}}{10 - w} = \infty$
Stardate 43989.1 converted into a calendar date in the TNG era 7 steps
Convert stardate 43989.1 into a calendar date using only the rule printed beneath the output. The console is in stardate-to-date mode on the TNG era, which pins stardate 41000 to the start of 2364 and hands every calendar year exactly 1000 stardates.
1. The rule is linear in the year and in the fraction of the year already elapsed, and f is confined below 1. That confinement is what makes it invertible: no stardate can be read as two different dates.
  
  $SD = 41000 + (Y - 2364 + f) \times 1000, 0 \leq f < 1$
2. Rearrange for the bracket. What you are solving for is the number of years since the start of 2364, carried to as many decimals as the stardate has.
  
  $\frac{SD - 41000}{1000} = Y - 2364 + f$
3. Substitute. The anchor comes off, the thousand divides out, and you are left with a plain count of years.
  
  $\frac{43989.1 - 41000}{1000} = 2.9891$
4. Split it. The integer part counts whole years past 2364, the remainder places you inside the year that follows them. Both halves fall out of the same division, so there is nothing to decide.
  
  $Y = 2364 + ⌊ 2.9891 ⌋ = 2366, f = 0.9891$
5. The fraction is a fraction of that calendar year, not of a fixed 365.25 days, so the year's length now matters. 2366 leaves a remainder of 2 when divided by 4, so it is a common year.
  
  $2366 = 4 \times 591 + 2 ⟹ 365 d$
6. Multiply to get elapsed days, and then count into the calendar. 361.02 elapsed days puts you inside day 362; 334 days reach the end of November in a common year, and the remainder is the day in December.
  
  $0.9891 \times 365 = 361.02 d ⟹ ⌊ 361.02 ⌋ + 1 = 362 = 334 + 28$
7. One more check that costs nothing. Since every year gets exactly 1000 stardates, the year you landed in occupies a block of 1000 consecutive numbers, and the meter under the output states that block.
  
  $41000 + (2366 - 2364) \times 1000 = 43000, 43000 + 999 = 43999$
Answer

28 December 2366, inside the stardate block 43000 to 43999. The consequence is that subtracting two stardates does not give you a duration. Each unit is a thousandth of its own calendar year, so you cannot convert until you know which years the two ends sit in. From 43989.1 to 44000.0 is 10.9 units, which here means 0.0109 of 365 days, or 3.98 days — and it lands exactly at midnight opening 2367, which is the check that the count into December was right. The identical 10.9 units taken inside 2368, a leap year, is 3.99 days instead: 15.7 minutes longer, because every unit there is worth 86.4 seconds more. The scale kinks every 1 January. The TOS rule carries no such kink: it divides a flat 365.25 days into 1000 and never consults the calendar again, which makes a TOS stardate a clock and a TNG one a calendar wearing a clock's numbers.

$1 SD = \frac{365}{1000} d \frac{366}{1000} d ⟹ Δ = 86.4 s$

References (1)

Insight block 3 — the instruction to invent each stardate: G. Roddenberry, Star Trek Guide, third revision, 17 April 1967, Desilu Productions — "pick any combination of four numbers plus a percentage point", with 1313.5 given as the worked example.

By the 42Math team · Updated 2026-07-29

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

All Tidal Zone lessons →

Example problems

voyager sprint - Voyager's top canonical speed — warp 9.975 — works out to roughly 85,000× the speed of light. At that pace, the 4.24-light-year trip to Proxima Centauri, our nearest stellar neighbor, would take about 26 minutes.
stardate now - Convert any Gregorian date into a TNG-era stardate using the show's own 1,000-stardates-per-year formula — see exactly what stardate the Enterprise crew would be logging on a given day.
borg encounter - Stardate 43989.1 marks 'The Best of Both Worlds' — the episode where Picard is assimilated by the Borg. Run it in reverse (stardate → date) to see exactly which real-world year that famous cliffhanger falls in.

YouTube

StarTalk·The Science of Star Trek with Dr. Charles Liu