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Dice notation

21d40

  • 21d40
  • 21 to 840
  • mean 430.5

Rolling 21d40 gives a total between 21 and 840, with a mean of 430.5 and a standard deviation of 52.8985. There are 4,398,046,511,104,000,000,000,000,000,000,000 equally likely ordered outcomes, and the most likely total is 430 or 431 at 0.749%.

The canonical address for this page is /21d40.

The roll

Notation21d40
Dice21
Faces per die40
Minimum total21all 21 dice showing 1
Maximum total840all 21 dice showing 40
Distinct totals820
Mean430.5n(f + 1)/2 + modifier, exact
Variance2,798.25n(f² − 1)/12, exact
Standard deviation52.89848769≈

Counting the outcomes

Ordered outcomes4,398,046,511,104,000,000,000,000,000,000,00040^21, every die distinguishable
Most likely total430 and 431two totals share the peak
Chance of that total0.748721%≈
Ways to roll it32,929,081,090,445,921,701,107,850,228,320exact count
Chance of the minimum2.27373675 × 10^-32%≈1 in 4,398,046,511,104,000,000,000,000,000,000,000
Chance of the maximum2.27373675 × 10^-32%≈1 in 4,398,046,511,104,000,000,000,000,000,000,000

Shape of the distribution

820 distinct totals, too many to list individually.

1st percentile308≈1.018% of rolls are this or lower
5th percentile343≈5.014% of rolls are this or lower
25th percentile395≈25.54% of rolls are this or lower
50th percentile430≈50% of rolls are this or lower
75th percentile466≈75.061% of rolls are this or lower
95th percentile518≈95.181% of rolls are this or lower
99th percentile553≈99.034% of rolls are this or lower

Chance of rolling at least

103100%≈
22699.9969%≈
43150%≈
6350.0034%≈
7589.26979907 × 10^-11%≈

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The same dice, different counts

The same count, different dice

Also reads as

#021D40 (colour)

  • #021D40
  • Blue
  • Dark
  • Nearest: Black

#021D40 is a blue with RGB values 2, 29, 64 and HSL 214°, 94%, 13%. It is a dark colour, so white text on it reaches 16.8:1 contrast (AAA for normal text). The nearest named colour is Black.

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Colour values

#021D40#021D40
HEX#021D40
RGBrgb(2, 29, 64)
RGB (0–1)0.0078, 0.1137, 0.251
RGB percentages0.8%, 11.4%, 25.1%
HSLhsl(213.9, 93.9%, 12.9%)
HSV / HSBhsv(213.9, 96.9%, 25.1%)
CMYK96.9%, 54.7%, 0%, 74.9%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer138,560
CSS custom property--colour: #021D40;

Brightness & contrast

Relative luminance0.01262WCAG 2.x, 0 is black and 1 is white
Perceived brightness31 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 16.77:1
Contrast with white16.77:1WCAG normal text: AAA
Contrast with black1.25:1WCAG normal text: Fail
Greyscale equivalent#1A1A1A
Inverted#FDE2BF

Colour vision & accessibility

Normal visionProtanopiaDeuteranopiaTritanopia
Protanopia#082041no red cones; affects about 1% of men; ΔE 2.3 from the original
Deuteranopia#001B3Fno green cones; the most common form, about 1% of men; ΔE 1.4 from the original
Tritanopia#00262Bno blue cones; rare, and affects men and women equally; ΔE 24.7 from the original
Distinguishable without hueYesnever rely on hue alone to carry meaning
Contrast with white, large text16.77:1WCAG large text: AAA
Contrast with black, large text1.25:1WCAG large text: Fail

Named colours

Black · ΔE 28.1Dark slateblue · ΔE 33Dark slate grey · ΔE 34.3Midnight blue · ΔE 35.9Dim grey · ΔE 42.2Steel blue · ΔE 43.2
Nearest named CSS colourBlack (#000000)ΔE 28.07, a distinctly different colour
Hue familyblue
CSS keyword usableNo exact keyword

Colour harmonies

base+30°+90°+120°+180°+210°+240°+270°+330°
Complementary#402502
Analogous#023C40, #060240
Triadic#40021D, #1D4002
Split complementary#400602, #3C4002
Tetradic#40023C, #402502, #024006

Tints, shades & saturation

+40%+30%+20%+10%base-10%-20%-30%-40%
Lighter +40%#1678F8
Lighter +30%#0760D4
Lighter +20%#054AA3
Lighter +10%#043371
Darker −10%#00070F
Darker −20%#000000
Darker −30%#000000
Darker −40%#000000
More saturated +25%#001D42
Less saturated −25%#0A1E38

Channel breakdown

R2
G29
B64
Red2 (0.8%)
Green29 (11.4%)
Blue64 (25.1%)
Hue213.87°
Saturation (HSL)93.94%
Lightness12.94%
Dominant channelBlue
Hex per channelR 02 · G 1D · B 40

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