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Free Black Scholes calculator and option pricing calculator to calculate option prices using the Black-Scholes formula. Use our black scholes calculator, option pricing calculator, black scholes model calculator, black scholes formula calculator, black scholes option calculator, black scholes call option calculator, black scholes put calculator, and option price calculator. Formula: C = S₀e^(-qT)N(d₁) - Ke^(-rT)N(d₂). Calculate option prices, Greeks (Delta, Gamma, Theta, Vega, Rho), and analyze options strategies with the Black-Scholes model. Our calculator uses the Black-Scholes formula to determine theoretical option prices for call and put options.
Last updated: February 2, 2026
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0.2265
Price sensitivity
0.0525
Delta sensitivity
8.6296
Volatility sensitivity
This option has significant time value, making it expensive but potentially profitable.
| Stock Change | New Stock Price | New Option Price | P&L |
|---|---|---|---|
| -10% | $90.00 | $0.01 | -$0.72 |
| -5% | $95.00 | $0.11 | -$0.62 |
| 0% | $100.00 | $0.73 | +$0.00 |
| 5% | $105.00 | $2.62 | +$1.89 |
| 10% | $110.00 | $6.07 | +$5.34 |
| 20% | $120.00 | $15.45 | +$14.72 |
Pricing model
Black-Scholes Formula
Calculate theoretical option prices using the Black-Scholes model
Risk measures
Delta, Gamma, Theta, Vega, Rho
Calculate all five Greeks for comprehensive options risk analysis
Call options
Bullish Strategies
Calculate call option prices and analyze bullish strategies
Put options
Bearish Strategies
Calculate put option prices and analyze bearish strategies
Strategy analysis
Complex Strategies
Analyze complex options strategies and combinations
Risk analysis
Risk Metrics
Calculate options risk metrics and portfolio analysis
For a $100 stock with $105 strike, 30 days to expiry, 5% risk-free rate, 20% volatility:
Call Option Price
$2.13
Delta
0.45
The Black-Scholes formula gives the theoretical price of European call and put options. Use this guide with our black scholes formula calculator or black scholes calculation tools.
C = S₀e^(-qT)N(d₁) - Ke^(-rT)N(d₂)Put: P = Ke^(-rT)N(-d₂) - S₀e^(-qT)N(-d₁). With d₁ = [ln(S₀/K) + (r - q + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T.
Quick example: S=49, K=50, T≈0.38, r=5%, σ=20% → Call ≈ $2.13. Our calculator does this black scholes calculation and all Greeks (Delta, Gamma, Theta, Vega, Rho) for you.
Our Black Scholes calculator implements the famous Black-Scholes-Merton model to calculate theoretical option prices and Greeks. The calculation applies the Black-Scholes formula to determine option prices based on current market conditions and option parameters.
C = S₀e^(-qT)N(d₁) - Ke^(-rT)N(d₂)Where d₁ = [ln(S₀/K) + (r - q + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T
Shows Black-Scholes option pricing and Greeks calculations
The Greeks measure how option prices change with various market factors. Delta measures price sensitivity, Gamma measures delta sensitivity, Theta measures time decay, Vega measures volatility sensitivity, and Rho measures interest rate sensitivity. These metrics help traders understand and manage options risk.
Need help with other options calculations? Check out our covered call calculator and portfolio risk calculator.
Get Custom Calculator for Your PlatformResult: Call Option Price = $2.13, Delta = 0.54
This call option is out-of-the-money with moderate time value and delta sensitivity.
Stock: $110, Strike: $105
Price: $7.85, Delta: 0.78
Stock: $100, Strike: $105
Price: $6.85, Delta: -0.46
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