Black-Scholes Call Option Calculator
The Black-Scholes model gives the theoretical fair value of a European call option from five inputs: the current asset price, the strike price, the time to expiration, the risk-free rate, and the volatility. This calculator returns the call price along with d1, d2, and delta, the rate at which the call value changes per unit move in the underlying. All inputs are editable so you can price any contract. The model assumes no dividends and constant volatility, so treat it as a baseline rather than a market quote.
Black-Scholes call formula
d1 = (ln(S / K) + (r + vol^2 / 2) * T) / (vol * sqrt(T))
d2 = d1 - vol * sqrt(T)
Call = S * N(d1) - K * e^(-r * T) * N(d2)
where N() is the standard normal cumulative distribution
N() is evaluated with a high-accuracy rational approximation. Delta equals N(d1) for a call. The rate and volatility are entered as decimals (5% is 0.05).
Worked example
With S = 100, K = 100, T = 1 year, r = 0.05, volatility = 0.20: d1 = (ln(1) + (0.05 + 0.02) * 1) / (0.20 * 1) = 0.35, d2 = 0.15. The call value is 100 * N(0.35) - 100 * e^(-0.05) * N(0.15) = 10.45 (rounded). Delta is N(0.35) = 0.64.
Black-Scholes call: frequently asked questions
What does the Black-Scholes call formula compute?
It gives the theoretical fair value of a European call option, the right to buy an asset at a fixed strike price on the expiration date. The price depends on the current asset price, the strike, the time to expiration, the risk-free interest rate, and the volatility of the underlying asset. The model assumes no dividends and constant volatility.
What are d1 and d2?
They are intermediate quantities in the formula. d1 measures how far the asset price is above the strike, adjusted for drift and volatility, in standard-deviation units; d2 equals d1 minus volatility times the square root of time. The call value is the asset price times N(d1) minus the discounted strike times N(d2), where N is the standard normal cumulative distribution.
What are the model's main limitations?
The standard Black-Scholes model assumes European exercise (only at expiration), no dividends, a constant risk-free rate, constant volatility, and lognormal price movements. Real markets violate these to varying degrees, which is why traders use it as a baseline and adjust with implied volatility surfaces and dividend corrections rather than treating its output as exact.
Sources
- The Black-Scholes-Merton option pricing model is a standard published result in financial mathematics (Black and Scholes, 1973; Merton, 1973). Options market structure background: U.S. Securities and Exchange Commission Investor.gov: Options.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.