Bitcoin calculators

Bitcoin Power Law · Calculators Bitcoin Power Law Calculators Your inputs Result Assumptions No financial advice. Models are no guarantee. What does this mean? Copy link Link copied ✓ Preparing … Your browser could not create the file. bitcoin-powerlaw-calculator Today's prices are not loaded yet. Please reload the page in a minute. Please check your inputs. at {price} already today not within {n} years in {n} years years Empty = today's price ({price}) Empty = {inst}'s current rate ({rate}) There is no current rate for this instrument yet – please enter one. Power Law: floor = {floor} × 10^{a} × days since 3 January 2009^{b} US dollars, the published formula, checked against every daily close since 2010; top band = floor × e^({height} ÷ (1 + (days ÷ {turn})³)), fitted through the cycle tops; trend (fair value) = the lower of floor ÷ {floor} and √(floor × top band). The model calculates in US dollars; converted to {cur} at today's rate (1 {cur} = {fx} USD). The model's prices are not adjusted for inflation. Today's Bitcoin price: {price} ({date}, OKX). Taxes are not considered. Floor zone Accumulation Fair Hot Euphoria Monthly savings Period Bitcoin you hold today Floor growth per day per week per month per year Fee per purchase Price path Expenses per month (today) Inflation per year Your age Retire at age Empty = as early as your Bitcoin allows. One-off purchase today Optional. Bought at today's price. Plan until age Monthly savings until then Optional. Bought at fair value. Withdrawal per month (today) Spread around the trend (σ) Standard deviation of ln(price ÷ trend). Measured since 2010: {sigma}. Half-life of a deviation Months until half of a deviation from the trend is gone. Number of runs What for Price today Sell at most Price increase per year Bitcoin as collateral Loan amount Interest per year Liquidation at LTV Loan-to-value at which the lender sells your collateral. Term Interest Amount Spread over months Bitcoin you sell Sell price Invest in Rate per year Tax on the dividend Share you sell Sell price Empty = today's top band. Buy-back price Empty = the floor in a year. Fee per sale and purchase Tax on the proceeds Unit Bitcoin price At fair value (Power Law trend) Today's price, rising with the trend At the floor (worst case) Stays at today's price At the top band (best case) House or flat Car Travel Something else are added to the loan I pay monthly Savings plan (DCA) How much Bitcoin a monthly savings plan buys and what it may be worth – depending on the price path. Your stack after {n} years of which bought: {btc} Invested Value at the end Value at the floor at the end Average buy price Value Value at the floor Invested One purchase a month, the first today, at the price of the chosen path; the fee ({fee}) comes off each purchase. Price path: Bitcoin costs exactly the model's fair value each month. Price path: today's price rising with the trend – today's ratio to fair value stays. Price path: Bitcoin costs only the floor each month – the model's worst case. Price path: Bitcoin stays at today's price. Price path: Bitcoin costs the top band each month – the model's line through the earlier cycle tops, its best case. Floor calculator How much the floor adds to your stack per day, week, month or year, and what your stack is worth in X years if Bitcoin only stands at the floor then. Your stack at the floor in {year} Floor then: {price} Floor today Your stack today At fair value in {year} Floor growth per year Your stack’s floor rises {per} In {year}, {per} 1 BTC: {n} What the floor adds to your stack {per} What the floor adds over a period is the floor at its end minus the floor at its start. Today it rises by about {pct} a day: the Power Law’s exponent {b} divided by the {days} days since 3 January 2009. That share shrinks slowly as the days add up, while the amount keeps growing with the floor. At fair value At the floor Value today The floor ran through the bear-market lows of 2015, 2018 and 2022; the model assumes it keeps rising along the Power Law. The price can also fall below it. Your stack stays the same: nothing bought, nothing sold. Retire with Bitcoin When can you stop working? The 4 % rule for Bitcoin: from then on you sell Bitcoin each month for your expenses, and it has to last for life even at the floor price. age {n} not by age {n} You can retire from retired at {n} Retiring at {n}, your Bitcoin lasts until age {n} for life (to {n}) you have {have} then, you need {need} Bitcoin needed to retire today you have {btc} Safe withdrawal rate in the first year of the stack at the floor; for stocks the rule says 4 % With the stock rule of 4 % only from needs 25 × your yearly expenses: {m}, today {btc} at the floor Selling at fair value already from Bitcoin left at {n} (sold at the floor) Expenses in the first year of retirement Needed to retire then Your Bitcoin, sold at the floor Your Bitcoin, sold at fair value The 4 % rule asks whether a fixed income, raised every year by inflation, lasts for the rest of your life. Here you sell Bitcoin for your expenses every month from retirement until age {n}. You can retire once your Bitcoin covers all of these sales at the floor price, the line the price has rarely been below. For stocks and bonds the safe rate is 4 % in the first year (Bengen 1994: it lasted 30 years in every US market since 1926). In the model the floor rises {now} this year and still {then} a year at age {n}, so with Bitcoin a much higher first withdrawal lasts. If the model breaks, it does not. Your expenses rise with inflation of {inf} a year, from today. Today you buy Bitcoin for {l} at today's price. Until you retire you buy Bitcoin for {m} each month at fair value. Monte Carlo simulator Thousands of possible price paths around the Power Law – and whether your stack carries your monthly withdrawals. Chance your stack lasts {n} years Bitcoin left (median) Value left (median) In a bad case (1 in 10) If it does not last, typically empty from Price, 10–90 % of runs Median Fair value Floor Bitcoin left, 10–90 % of runs Bitcoin left, median {runs} simulated price paths, month by month. Each starts at today's price and strays from the trend like Bitcoin since 2010: spread σ = {sigma} in ln(price ÷ trend), half of a deviation is gone after {hl} months (measured on the daily closes: σ = {fsigma}, {fhl} months). Each month you sell Bitcoin for {w}, rising with inflation of {inf} a year. The same inputs always give the same runs, so a shared link shows the same result. Upgrade calculator House, car, travel: from when you can afford it without selling more than X % of your stack. Share of your stack today Bitcoin price at which it costs {x} Fair value reaches it Even the floor reaches it that is {btc} Share needed at fair value Share needed at the floor Your limit The price of the {what} rises by {inf} a year. Share = price ÷ (your stack × Bitcoin price). Taxes and fees on the sale are not considered. Borrow instead of sell A loan with Bitcoin as collateral: loan-to-value, liquidation price and how far it stays from the floor. Loan-to-value (LTV) today Liquidation price today Liquidation price after {n} years Floor above the liquidation price (at its closest) The floor stays above it for the whole term. In {n} of {m} months the liquidation price is above the floor – a fall to the floor would liquidate you. Interest over {n} years Selling instead costs today Liquidation price Floor Fair value Price today The lender sells your collateral when the loan reaches {liq} of its value: liquidation price = debt ÷ ({liq} × Bitcoin as collateral). Interest is added to the loan: the debt grows by {i} a year (compounded monthly). You pay the interest ({m} a month) from other income; the debt stays the same. Lenders' terms (margin calls before liquidation, fees, custody) differ; the risk that the lender fails is not included. Lump sum vs. DCA All at once or spread over months? How often a lump sum ends with more Bitcoin – depending on the zone the price is in today. Chance a lump sum today ends with more Bitcoin Zone today A lump sum today buys Spread over {n} months buys (median) Lump sum's advantage (median) Chance the lump sum wins, by starting zone 50 % Lump sum: everything at today's price. DCA: {n} equal monthly purchases, the first today. Compared is who ends with more Bitcoin. Per zone, 1’000 simulated price paths start at a typical price of that zone ({ratios} fair value) and stray from the trend like Bitcoin since 2010 (σ = {sigma}, half-life {hl} months). The highlighted zone is today's. Digital-credit cash flow Sell X Bitcoin at price Y, put the proceeds into a Bitcoin-backed preferred share such as STRC, STRK, STRD, STRE, SATA or Metaplanet's: this is the dividend per month and year. Dividend per month Dividend per year Proceeds of the sale Dividends over {n} years Kept, {btc} would be worth in {year} (fair value) Proceeds + dividends Bitcoin kept, at fair value Bitcoin kept, at the floor {inst}'s rate: its current dividend rate ({div}) on the stated value ÷ its price = {rate} (as of {date}, price from Yahoo Finance), as on the Digital Credit page. {inst} is not listed: its rate is the dividend rate on the stated value ({rate}, as of {date}). Rate as entered: {rate} a year. The preferred share keeps its price and its rate; dividends are not reinvested. Paid in {currency}, converted at today's rate. {inst} pays {freq}; per month is a twelfth of the year. Per month is a twelfth of the year. The US tax treatment (e.g. return of capital) does not automatically apply in Germany, Austria or Switzerland. Sell the top, buy back at the floor Sell part at the high and buy back lower: how much Bitcoin you have afterwards – and from which buy-back price it does not pay. Bitcoin afterwards You sell Proceeds after fee and tax Buying back gets you Only pays when buying back below If the price never comes back {btc} and {cash} Bitcoin afterwards, by buy-back price Bitcoin today Your buy-back price Sell price {price}; without an input today's top band, the model's curve through the cycle tops. Buy-back price {price}; without an input the floor in a year. Selling and buying back each cost the fee; the tax is a share of the proceeds. The risk: the price may never fall to your buy-back price. Sats converter Euros, francs or dollars in sats and Bitcoin – and back. Plus: how many sats the same amount bought before and buys in future according to the model. In sats In Bitcoin In {cur} 1 {cur} buys What the amount bought (1 January) At fair value (model) 1 Bitcoin = 100’000’000 sats. History: the first daily close of each year in US dollars (Coin Metrics, OKX), converted at today's exchange rate. Future: the model's fair value on 1 January each year. Forecast: what if … What happens to the price if only a little bitcoin is left on exchanges – or a state or the pension funds start buying? A thought experiment with your own assumptions and an open formula. Bitcoin on exchanges today About 2 million, the figure going round on X; on-chain trackers count somewhat more. Of it left on exchanges Empty: as many as today. Try 500’000, 100’000 or 0. Who buys They buy Spread over Price reaction k 1: half as much on offer, twice the price. 0.5: ×1.4. 2: ×4. Nobody else USA Germany Austria Switzerland Poland Philippines Pension funds worldwide All of them together Empty: {rule} nobody buys. Type an amount and someone does. {n}, as the BITCOIN Act proposes for the USA. {n}, as much per inhabitant ({pop} million) as the USA's million. {n}: 1 % of the world's pension assets (about 58 trillion dollars) at today's price. {n}: every state in the list and the pension funds together. {n} are bought, your amount. Price in {year} with your scenario × {m} the price without it Left on exchanges then Price in {year} without it Bought {p} of all 21 million What the buyers pay With your scenario Without it Formula: price = price without the scenario × (on exchanges today ÷ left on exchanges)^k. With k = {k} that is ×{m} by {year}. Buyers take what they buy off the exchanges, evenly over {y} years. Without the buyers, the exchanges' supply goes from {ex} to {left} in the same time. The buyers want {buy}, but only {have} are on exchanges. They would have to buy the rest from holders – at whatever price those name. No exchange price can be calculated for that. Buying done A game with your assumptions, not a forecast: in reality holders sell into rising prices, miners add new coins and buyers also buy outside exchanges. Nothing left on exchanges: then there is no exchange price any more. Whoever still wants bitcoin has to talk a holder into selling – at whatever price they name. Mining calculator Pool fee Hardware cost Big mining farms' power price per kWh What the large farms that make up most of the network pay. Surveyed miners paid a median of USD 0.045 (Cambridge, 2025). At today's price the network would stop growing at {even}. Network hashrate, EH/s Mining income Hashrate How far: the big farms count a bitcoin at the price the price path has a year ahead. The network grows while their running costs are below what mining pays at that value, the slower the closer the two come, and shrinks above that. Assumed: power at {fe} per kWh and {other} per kWh for their other running costs. The machines running today need {j} J per TH. A machine never gets better, so the network improves only through new machines, each year's {eff} more efficient than the last, and through old ones leaving after {life} years: {end} J per TH in {month}. New machines take time to arrive and old ones go off gradually: in a year the network covers {year} of the distance. Farms keep bitcoin to sell them higher later; the model counts that by valuing a bitcoin at the price a year ahead. Power, personnel and new machines are still paid in money, so in the meantime the farms sell, borrow or issue shares. Profit per month, today {rev} mined − {cost} power Bitcoin per month, today {sats} a day Pays off up to a power price of {price} per kWh Mined in {n} years worth {value} when mined Net profit Mined and kept in {n} years worth {value} at the floor of {month} Paid in money {hw} hardware + {power} power Bitcoin kept, {at} at the floor at fair value at the top band Your miner Hardware lifetime Scenario Running hours a day, averaged over the year Home Mining Solar Heater Whales Whales: a mining farm runs its machines {h} hours a day on industrial power at {price} per kWh. The farm: {n} of these machines, {ph} PH/s, drawing {mw} MW; their hardware costs {hw}. Per machine. Your farm's hashrate Personnel per machine and month Technicians, security and management. A large farm employs about one person per 300 to 500 machines. Rent per machine and month Building, racks, fans and the grid connection. Hosting charged about USD 0.015 to 0.03 per kWh on top of power in 2025 for personnel, rent and its margin. Repairs per year Of the hardware's price: machines whose hashboards, fans or power supplies fail are repaired, a hashboard for about USD 150. Tax on profit 21 % is the US federal corporate tax; most of the network's hashrate is in the US. Sell what pays the running costs, keep the rest Left stacked after {n} years of {mined} mined; worth {value} at the floor of {month} Sold to pay running costs Sold around the top band for {money}: the price of {n} machines like these today; {left} still kept {power} power + {other} personnel, rent and repairs + {tax} tax {hw} hardware + {power} power + {other} personnel, rent and repairs + {tax} tax {rev} mined − {cost} power − {other} personnel, rent and repairs Hardware Hardware and running costs Running costs besides power: {staff} personnel and {rent} rent per machine and month, repairs of {fix} of the hardware's price a year, and {tax} tax on the profit: the mined bitcoin at the month's price less the running costs and the hardware written off over its lifetime. Losses are set against later profits. Selling what pays the running costs: the hardware is paid once in money, then the farm has no other money. Each month it sells as many of the mined bitcoin as pay its running costs and tax at that month's price on the price path, which in bad years is below the fair value, and keeps the rest. In months with the price at or around the top band (above the middle between fair value and top band) it sells what it kept as well: the money for new machines. The bitcoin paid their running costs throughout the machines' lifetime. Selling what pays the running costs: the hardware is paid once in money, then the farm has no other money. Each month it sells as many of the mined bitcoin as pay its running costs and tax at that month's price on the price path, which in bad years is below the fair value, and keeps the rest. In months with the price at or around the top band (above the middle between fair value and top band) it sells what it kept as well: the money for new machines. In {month} the bitcoin the machines mine no longer pay their running costs, and the farm switches them off: from then on buying bitcoin is cheaper than mining them. The miner keeps running also in months whose power costs more than it earns. Not included: the hardware's resale value and the cost of financing it. Home mining: the miner runs {h} hours a day on household electricity at {price} per kWh. Solar: the miner runs {h} hours a day. Your solar system ({pv}, {bat}) covers about {sun} of its power; the rest comes from the grid at {price} per kWh. Heater: in the heating season the miner heats a room in place of an electric heater, on average {h} hours a day over the year. You pay for that power to heat anyway, so it costs {price} extra per kWh. This holds only in place of an electric heater, not a gas heater or a heat pump, and with a quiet miner. In place of an electric heater, its power costs nothing extra. Power of the heater it replaces A fan heater draws about {w} W. Your solar system {kwp} kWp nominal power, about {kwh} kWh a year; installed for about {cost}. What the panels make sets how much of the miner's power they carry. Battery storage Carries the day's surplus into the night; installed for about {cost}. Follows the solar system until you choose one yourself. Add the solar system's price to the hardware cost Balcony solar 800 W House roof 5 kWp House roof 10 kWp House roof 15 kWp No battery The solar share is a rough estimate over the year's average day: a solar system yields about {yield} kWh per kWp a year; in daylight it carries at most {day} of a load running day and night, and a battery carries the day's surplus into the night, {trip} of it arriving. Your household's own use of the solar power is not counted. The solar system and its battery, {cost}, count as hardware. Yes No Any: the sun covers all of its power Miner switched off Bought at fair value + 10 % fee Compare with buying bitcoin Mining only Compare: buying bitcoin instead The miner draws {w} W, far less than the {heater} W heater. That only works in special cases, for example in place of a towel heater. {w} W is more than a household socket here carries for hours ({max} W): this miner needs its own dedicated power circuit. A machine for mining farms: very loud and power-hungry, hardly practical in a normal home. Miner: {name} with {th} TH/s and {w} W, bought for {hw}. The miner runs for {n} years, until {month}. After that it is switched off: it uses no more power and mines no more bitcoin; the bitcoin it mined are kept to the end of the period. Stack and hold: hardware and power are paid in {cur}, no bitcoin is sold for them. The mined bitcoin pile up and count at the price path you choose under the chart. The Power Law floor rises over time: {floor} in {month}. Keep them (stack and hold) Sell them each month Mined bitcoin Hardware paid off in {month} Buying instead {money}, what mining costs in money, each amount bought at the fair value plus 10 % fees and costs when it is paid Mined, at the month's price Hardware and power Halving Network: {hash} EH/s today, about {end} EH/s in {month}. The hashrate doesn't grow by a fixed rate: it follows what mining pays (block reward × the price path's price), so it falls after a halving and when the price falls, and rises with the price and with better devices. Your share of the blocks is your hashrate divided by the network's. Per block: {sub} new bitcoin + {fees} in fees (average of the last day). The new bitcoin halve at every halving; the next is expected in {month}. The pool keeps {fee} and pays out evenly. Not included: cooling, repairs, the hardware's resale value and taxes. Solo mining: the mining lottery Mine on your own and every block is a lottery ticket: whoever finds it keeps the whole reward. How likely is that with your miner, what does a win pay and what does the electricity cost? Chance of finding a block within a year Chance per day On average one block every A block pays you Electricity per year In a pool instead, in the first year 1 in {n} {n} days {n} years {v} after electricity Chance of at least one block so far The network's hashrate is not loaded yet. Please reload the page in a few minutes. The network's hashrate today: {net} (mempool.space's estimate); your miner has {share} of it. The network grows as in the mining calculator, with bitcoin at the floor: to {end} by {month}. Your share of the blocks shrinks with it, so the chance over the years is lower than today's pace suggests, and the average wait is today's. A block pays {btc}: new bitcoin plus {fees} in fees, the average of the last {n} blocks. Each halving cuts the new bitcoin in half. Every attempt has the same chance, however long you have mined: the average is no promise. The block can come tomorrow or never. A pool shares its blocks by hashrate: a small, steady income instead of the lottery, before the pool's fee. Your miner's hashrate Its power draw Electricity price per kWh Currency Transaction fee What does sending bitcoin cost right now? The network's live fee rates for a slow, standard or fast confirmation, in sat/vB, in sats and in your currency, for a transaction of your size. Standard: in about 30 minutes Fast: next block, about 10 minutes Slow: in about an hour Transaction size {i} × input, {o} × output Slow Standard Fast Your transaction The network's fee rates are not loaded yet. Please reload the page in a few minutes. Fee rates from the transactions waiting in the mempool (mempool.space's recommendation, as of {time}): fast {fast}, standard {standard}, slow {slow}. They change from minute to minute with the demand for space in the blocks; your wallet may suggest slightly different rates. Fee = rate × size. Size = {base} vB + {in} vB per input + {out} vB per output ({type}). The fee depends on this size, not on the amount you send. Inputs (coins you spend) Each amount you once received counts as one. Paying from a single one: 1. Outputs (recipients and change) One payment with change back to you: 2. Address type Native SegWit (bc1q…) Taproot (bc1p…) Nested SegWit (3…) Legacy (1…)