Put Price (other side)
$5.57
Black-Scholes Option Calculator
Price European call and put options using the Black-Scholes model.
Call Option Price
$10.45
Intrinsic Value
$0.00
Time Value
$10.45
How to use the Black-Scholes Option Calculator
The Black-Scholes Option Calculator is free and runs entirely in your browser — no sign-up, and nothing you enter leaves your device. It opens pre-filled with a realistic example, so you can see how it works before replacing any figure with your own; the results update as you type. Press Calculate to refresh the result panel, or Reset to return to the example.
The inputs it asks for:
- Stock Price (S) — a dollar amount.
- Strike Price (K) — a dollar amount.
- Time to Expiration (Years) — a number.
- Risk-Free Rate — a percentage (enter 6 for 6%).
- Volatility (σ) — a percentage (enter 6 for 6%).
- Option Type — choose one — Call, Put.
The formula
The Black-Scholes model prices a European option from five inputs — the stock and strike prices, time to expiry, the risk-free rate and volatility — by weighing the odds the option finishes in the money against the discounted cost of exercising:
Call = S·N(d₁) − K·e^(−rT)·N(d₂) (put by symmetry)
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ − σ√T- S, K
- the stock (spot) and strike prices
- T, r, σ
- time to expiry in years, the risk-free rate, and volatility
- N()
- the standard normal cumulative distribution
It assumes European exercise (only at expiry), no dividends, and constant volatility — simplifications real markets break. Volatility is the one input you can't observe directly and the one the price is most sensitive to; the model splits the premium into intrinsic value and time value.
Worked example
Using the example values — Stock Price (S) $100.00, Strike Price (K) $100.00, Time to Expiration (Years) 1, Risk-Free Rate 5%, Volatility (σ) 20%, Option Type Call — the Black-Scholes Option Calculator returns a Call Option Price of $10.45. It also reports Put Price (other side) ($5.57), Intrinsic Value ($0.00), Time Value ($10.45).
Prefer your own numbers? Change any field above and this recomputes instantly.
Key terms
- Call / put
- The right to buy (call) or sell (put) at the strike price.
- Strike price (K)
- The price at which the option can be exercised.
- Volatility (σ)
- How much the stock's returns swing — the key, unobservable input.
- Intrinsic vs time value
- Intrinsic is the in-the-money amount now; time value is the rest of the premium.
Frequently asked questions
What is volatility and why does it matter so much?
It's the expected variability of the stock's returns. Higher volatility raises both call and put prices because it widens the range of favourable outcomes — and it's the input the price is most sensitive to.
Does this handle American options or dividends?
No — it's the plain European, no-dividend model. American options (exercisable any time) and dividend-payers need adjusted models.
What's the difference between intrinsic and time value?
Intrinsic value is what the option is worth if exercised now; time value is the extra premium for the chance it moves further in your favour before expiry. They sum to the option price.