As an attempt to resolve an apparent problem while conducting real transactions in Bitcoin with lightning. I've derived a simplified list of prices of dollars denominated in round numbers of Sats (bitcoin). This allows a person to reduce constant consultation of the transient market price of Bitcoin.
To use this list, you check the price of bitcoin periodically and find the row where the current price is between "$/BTC Low" and "$/BTC High", and write down the number of Sats per dollar in a predominant place along with the time.
When transacting, for example, if you want to pay $10.00 in sats, multiply the two to yield the amount. If the present price per bitcoin is $54,321.09, the number of sats per dollar from the table is 1860. $10 is 18600 sats. $3.21, calculated is 5970.6, and rounded is 5971.
The prime advantage of this mechanism is the number 1860 is the only number you need to remember and this number will only change a few times per day by a whole number amount. Your dollar-transaction can be multiplied by this memorized number.
The list below is computed from a spreadsheet, that I've posted here based on a maximum +/-2.5% exchange rate error between dollars and bitcoin. This could be useful for small day-to-day transactions and if the rate is updated periodically (assuming the price is random), every few hours, the net gain and loss should eventually average to zero.
Sat/$$/BTC Low$/BTC High
3300$30,076.89$30,536.13
3250$30,536.13$31,009.62
3200$31,009.62$31,498.02
3150$31,498.02$32,002.05
3100$32,002.05$32,522.47
3050$32,522.47$33,060.11
3000$33,060.11$33,615.82
2950$33,615.82$34,190.53
2900$34,190.53$34,785.24
2850$34,785.24$35,401.00
2800$35,401.00$36,038.96
2750$36,038.96$36,700.34
2700$36,700.34$37,386.44
2650$37,386.44$38,098.69
2600$38,098.69$38,838.61
2550$38,838.61$39,607.84
2500$39,607.84$40,408.16
2450$40,408.16$41,241.50
2400$41,241.50$42,109.93
2350$42,109.93$43,015.73
2300$43,015.73$43,961.35
2250$43,961.35$44,949.49
2200$44,949.49$45,983.09
2150$45,983.09$47,065.34
2100$47,065.34$48,081.37
2060$48,081.37$49,024.32
2020$49,024.32$50,005.00
1980$50,005.00$51,025.72
1940$51,025.72$52,088.99
1900$52,088.99$53,197.51
1860$53,197.51$54,354.25
1820$54,354.25$55,562.42
1780$55,562.42$56,825.52
1740$56,825.52$58,147.40
1700$58,147.40$59,532.25
1660$59,532.25$60,608.29
1640$60,608.29$61,352.00
1620$61,352.00$62,114.20
1600$62,114.20$62,895.57
1580$62,895.57$63,696.85
1560$63,696.85$64,518.81
1540$64,518.81$65,362.27
1520$65,362.27$66,228.07
1500$66,228.07$67,117.12
1480$67,117.12$68,030.36
1460$68,030.36$68,968.80
1440$68,968.80$69,933.49
1420$69,933.49$70,925.55
1400$70,925.55$71,946.17
1380$71,946.17$72,996.59
1360$72,996.59$74,078.14
1340$74,078.14$75,192.22
1320$75,192.22$76,340.33
1300$76,340.33$77,524.04
1280$77,524.04$78,745.04
1260$78,745.04$80,005.12
1240$80,005.12$81,306.19
1220$81,306.19$82,650.27
1200$82,650.27$84,039.55
1180$84,039.55$85,476.33
1160$85,476.33$86,963.10
1140$86,963.10$88,502.51
1120$88,502.51$90,097.40
1100$90,097.40$91,750.84
1080$91,750.84$93,466.11
1060$93,466.11$95,246.73
1040$95,246.73$97,096.53
1020$97,096.53$99,019.61
1000$99,019.61$101,020.41
Feel free to print this table out on a paper and use it to update your posted exchange rate.
Comment below to request a refreshed file link.
I can't get the cashier to figure out the proper change when I give them a $5.02 when the amount I'm owing is $4.77. So I definitely don't want to trust them to be calculating the amount of sats using some simplification method you describe.
Who do you suspect would be doing this?
Or, the alternative ... get a $400 device that displays moscow time.
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This isn't necessarily for the cashier, its for someone wanting to have a basis for transitioning from pricing in dollars to sats. If you use a number that only needs to change when there is a 5% swing in bitcoin price, it will likely only change once or twice per day and more commonly once per week.
Lets say you want to buy a freezedryer for $4000, but wonder how much bitcoin that is. By the time you look up the price of bitcoin and try to figure the amount of bitcoin, you've probably already forgotten why you were looking up the price of bitcoin and getting wrapped around the axle about the change in price. If you have a number in mind that only changes every few days, and its 'good enough' for a rule of thumb, you can more likely than not do the calculation in your head.
For example:
  • The freezedryer is $3999 plus tax, that's close to $4000
  • $4000 times 2300 sat/$
  • that's 5 zeros and 4 x 23
  • 23 x 2 is 46
  • 46 x 2 is 92
  • the freezedryer is 92 and 5 zeros
  • subtract 3 zeros for ksats, that leaves two zeros, so its 9200 ksats.
  • you know 1000 ksats is 0.01 bitcoin, so its 0.092 BTC or about 0.1 BTC
You don't even need to consult your phone, and if you get used to thinking of prices in sats, this is what is required in the process of rebasing an economy to a new currency, or 'thinking in bitcoin'.
If you're negotiating price for something with another person, you can get them to agree to use the rounded sats per dollar for pricing, and do the exchange in sats rather than dollars.
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Rough numbers to memorize: 1000 sats/$ at about 100k 2000 sats/$ at about 1/2 100k 3000 sats/$ at about 1/3 100k
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I found an error in my calculations, an off by factor-2. This version provides a more granular increment in sats per dollar and yields an average error range of +/-1.7%, and maximum of 2.4%
Here is a more concise table.
$/BTC From$/BTC Up toSat/$
$29,857.40$30,776.523300
$30,776.52$31,754.033200
$31,754.03$32,795.703100
$32,795.70$33,908.053000
$33,908.05$35,098.522900
$35,098.52$36,375.662800
$36,375.66$37,749.292700
$37,749.29$39,230.772600
$39,230.77$40,833.332500
$40,833.33$42,572.462400
$42,572.46$44,466.402300
$44,466.40$46,536.802200
$46,536.80$48,199.772100
$48,199.77$49,390.242050
$49,390.24$50,641.032000
$50,641.03$51,956.821950
$51,956.82$53,342.821900
$53,342.82$54,804.801850
$54,804.80$56,349.211800
$56,349.21$57,983.191750
$57,983.19$59,714.801700
$59,714.80$61,553.031650
$61,553.03$63,508.061600
$63,508.06$65,591.401550
$65,591.40$67,816.091500
$67,816.09$70,197.041450
$70,197.04$72,751.321400
$72,751.32$75,498.581350
$75,498.58$78,461.541300
$78,461.54$81,666.671250
$81,666.67$85,144.931200
$85,144.93$88,932.811150
$88,932.81$93,073.591100
$93,073.59$97,124.001050
$97,124.00$101,051.341010
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What the spreadsheet tells us is that you will have better than 2.5% accuracy if you:
  • round to the nearest hundred sats/$ when bitcoin is between 4000 and 2100 sats/$ ($25k to about $48k)
  • round to the nearest fifty sats/$ when bitcoin is between 2100 and 1000 sats/$ (about $50k to $100k)
Another way to put it is "above 2100 sats/$, round to nearest 100, below 2100 sats/$ round to nearest 50."
This works up to $100k/BTC
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