QF-Learn

Black-Scholes calculator with Greeks and implied volatility

This calculator prices European call and put options with the Black-Scholes-Merton formula and shows all five Greeks, the implied volatility for a market price, and a chart of the option’s value. Change any input and everything updates at once, in your browser.

Call price10.4506
Put price5.5735
d₁0.3500
d₂0.1500
Option Greeks for the inputs above
GreekCallPutUnits
Delta0.6368-0.3632per 1.00 move in S
Gamma0.01880.0188delta per 1.00 move in S
Vega0.37520.3752per 1 point of volatility
Theta-0.0176-0.0045per calendar day
Rho0.5323-0.4189per 1 point of rate

Implied volatility solver

Implied volatility24.11%

Uses the stock, strike, days, rate and dividend above. “No solution” means the price is below the option’s minimum value or above its maximum.

Call value today and at expiryThe Black-Scholes value of the call across stock prices from 60 to 140, and its payoff at expiry, for the inputs above.020406080100120140Strike 100Stock priceCall valueValue with 365 days leftPayoff at expiry

The CSV covers stock prices from 60% to 140% of the strike, under a CC BY 4.0 licence. The address bar holds your inputs, so you can share or bookmark them.

How to use it

  1. Enter the stock price, the strike, and the number of calendar days until expiry.
  2. Enter the volatility and the risk-free rate as annual percentages (20 means 20%).
  3. For a stock or index that pays dividends, enter its continuous dividend yield; otherwise leave it at 0.
  4. To find implied volatility, choose call or put and type the option’s market price.

Check it against a known value: stock 100, strike 100, 365 days, 20% volatility, 5% rate and no dividend give a call of 10.4506 and a put of 5.5735, the same as the worked example in the Black-Scholes model explained.

The formula it uses

C = Se−qTN(d1) − Ke−rTN(d2)
P = Ke−rTN(−d2) − Se−qTN(−d1)
d1 = [ln(S/K) + (r − q + σ²/2)T] / (σ√T),  d2 = d1 − σ√T

T is the days to expiry divided by 365. The Greeks are the formula’s exact derivatives, shown the way traders quote them: vega and rho per one percentage point, theta per calendar day. What each one means is explained in option Greeks explained, and how the implied volatility is solved in implied volatility. The normal distribution is computed to about fifteen decimal places, so prices agree with scipy to the last digit shown.

What it does not do

It prices European options, which can only be exercised at expiry. American options can be worth more, puts especially; use a binomial tree for those. It also uses one volatility for every strike, so it will not reproduce a market’s volatility smile. It is a learning and checking tool, not trading advice.

Cite or reuse this calculator

You are welcome to link to this page from course notes, assignments, articles or answers. The CSV export is free to reuse under the Creative Commons Attribution 4.0 licence: credit QF-Learn with a link to this page.

Tolenaar, D. (2026). Black-Scholes calculator with Greeks and implied volatility. QF-Learn. https://qf-learn.app/tools/black-scholes-calculator

Practise options pricing in the QF-Learn app

QF-Learn teaches Black-Scholes, the Greeks and volatility in five-minute lessons, with quizzes and a game, Volatility Surfer, where you practise estimating volatility. It is free and coming to Android and iOS.