How the model works
The calculator treats ETH's log returns as normally distributed with zero expected drift. Over a period of T years with annualized volatility σ, the spread of outcomes is σ√T. The chance of finishing above a target K from price S is N((ln(S/K) − σ²T/2) / (σ√T)), where N is the standard normal distribution. This is the same math behind option pricing, minus interest rates.
The "touch" column uses the reflection principle: for a driftless path, the probability of hitting a level before the deadline is roughly twice the probability of finishing beyond it. Options traders use the same rule of thumb.
How to use the result responsibly
- Sense-check headlines. If someone says $10,000 ETH is "guaranteed" this year, see what move that implies and how unusual it is at realistic volatility.
- Size positions for both tails. The same math that gives upside odds gives downside odds. Check the $1,500 or $2,000 row before adding leverage. Our position-sizing guide covers this, and the ETH drawdown history shows how deep past falls went (−94% in 2018, −79% in 2022).
- Prefer process over targets. A plan like dollar-cost averaging doesn't depend on calling a price. Try the ETH DCA calculator.
- Read the fundamentals. See Is Ethereum a good investment? and our ETH risk guide.
Frequently asked questions
Is this an Ethereum price prediction?
No. It is a probability model, not a forecast. It assumes ETH has no expected drift and that its daily moves follow a lognormal distribution with the volatility you choose. Real crypto returns have fatter tails, regime changes and news shocks, so treat the output as a rough sense of scale, not a signal to buy or sell.
What volatility should I use?
Ethereum's annualized realized volatility has historically ranged roughly from 40% in quiet periods to over 100% in crashes and manias; a long-run average around 60–80% is a common reference. Higher volatility makes distant targets (both up and down) more likely. Try several values to see how sensitive the answer is.
What is the difference between "finish above" and "touch"?
"Finish" is the chance ETH is above (or below) the target on the chosen date. "Touch" estimates the chance the price hits the target at any moment before that date, which is always higher. The touch figure uses a standard reflection-principle approximation (about twice the finish probability) and is less precise.
How do prediction markets compare?
Markets such as Polymarket or Kalshi list contracts like "Will Ethereum reach $X by December 31?". Their prices reflect traders' collective view, including drift and sentiment that this model ignores. Comparing the two can show where the market is more bullish or bearish than a neutral volatility model. Check local laws before using any prediction market.
Does this tool use my data?
No. Calculations run in your browser. The current ETH price is pulled from a public price feed; if it is unavailable, a reference price is used and labeled, and you can type your own starting price.