Option Premium Calculator
The option premium is the price of an option contract: what the buyer pays and the seller receives for the right to buy or sell the underlying at the strike price before expiry. Enter the underlying price, strike, time to expiration, risk-free rate and volatility to get the Black-Scholes theoretical premium for a European call or put, split into intrinsic value and time value, with the total cost for one contract.
Option premium
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Theoretical value from the Black-Scholes model for a European option on a non-dividend-paying underlying. Market prices also reflect supply, demand and dividends, so treat this as a fair-value estimate, not a quote.
Quick Answer
A call option on a $100 stock with a $105 strike, 3 months to expiry, a 5% risk-free rate and 20% volatility has a Black-Scholes theoretical premium of $2.48 per option, or $247.79 for one 100-share contract. It is out of the money, so the intrinsic value is $0.00 and the entire $2.48 is time value. The calculator above is pre-filled with this exact contract.
Key takeaways
- Every premium splits into two parts: intrinsic value (what the option is worth if exercised now) plus time value (what buyers pay for the chance of a bigger move before expiry).
- Premiums are quoted per share but paid per contract. A $2.48 premium on a standard 100-multiplier contract costs $247.79 of actual cash, which is the figure that decides position size.
- This tool prices European options on non-dividend-paying underlyings with constant volatility and rates, the textbook Black-Scholes assumptions. US equity options are American-style and most stocks pay dividends, so treat the answer as a fair-value estimate, not a quote.
- Volatility is the only input you cannot observe. Because the model inverts cleanly, traders often run the formula backwards: given a market price, what volatility is implied. That implied number is the market's forecast in disguise.
How to use the option premium calculator
Pick the option type, enter the five Black-Scholes inputs and the contract multiplier, then click Calculate. The results stay hidden until you click.
- Option type: call for the right to buy, put for the right to sell. The formula flips between the two, so this choice changes everything downstream.
- Underlying and strike prices: the current price of the stock or index, and the contract's strike. Their relationship decides moneyness: a call is in the money when the underlying is above the strike, a put when it is below.
- Time to expiration in years: enter a decimal, not days or months. Three months is 0.25, six months is 0.5, one year is 1. The old version of this page said days or months were acceptable; they never were, and this version says so on the label.
- Risk-free rate and volatility: enter both as percents (5 means 5%). Use a Treasury yield for the rate and a historical or implied volatility for sigma. Volatility moves the premium more than any other input you have to estimate.
- Contract multiplier: 100 for standard US equity options. The per-option premium times this number is the cash that changes hands for one contract.
Once you know what the contract costs, the next question is how many contracts your risk budget allows. The option position size calculator turns that premium into a position size from your account risk.
The formula: Black-Scholes in plain language
The Black-Scholes formula values a European option as the discounted expected payoff under risk-neutral probabilities, computed through the cumulative normal distribution of two intermediate values, d1 and d2.
Put: P = K·e−rT·N(−d₂) − S·N(−d₁)
d₁ = [ln(S/K) + (r + σ²/2)·T] ÷ (σ·√T)
d₂ = d₁ − σ·√T
Premium = Intrinsic value + Time value
Read it in three layers. First, d1 and d2 measure how far the option is from the money in volatility-adjusted terms: d2 is often interpreted as the risk-neutral probability of finishing in the money. Second, N(d1) and N(d2) convert those distances into probabilities through the normal distribution, and the e−rT term discounts the strike back to today's money. Third, the premium splits: intrinsic value is max(0, S − K) for a call and max(0, K − S) for a put, the profit from exercising right now, and time value is whatever remains. The call put premium calculator focuses on that premium figure itself, while the option Greeks calculator extends the same model into delta, gamma, theta and vega.
The honest limits belong next to the formula. The model assumes the option is European (exercisable only at expiry), the underlying pays no dividends, volatility and the risk-free rate stay constant, and markets are frictionless. Real equity options are American-style, most large stocks pay dividends, and volatility smiles. The approximation inside this tool, the Abramowitz and Stegun formula 7.1.26 for the normal CDF, is accurate to about one part in ten million, so any gap between this tool and a market quote comes from the model's assumptions, not its arithmetic.
Worked example: the $100 / $105 call, plus three more runs
The pre-filled run is a call with S = 100, K = 105, T = 0.25 years, r = 5% and volatility = 20%. Every row below is a verified run of the calculator above.
| Run | Premium | Contract total | Intrinsic | Time value |
|---|---|---|---|---|
| Worked example: call, S=100, K=105, T=0.25, r=5%, vol=20% | $2.48 | $247.79 | $0.00 | $2.48 |
| Same contract as a put | $6.17 | $617.36 | $5.00 | $1.17 |
| ITM call: S=150, K=140, T=0.5, r=4%, vol=30% | $19.56 | $1,956.45 | $10.00 | $9.56 |
| ATM put, 1 year: S=100, K=100, T=1, r=5%, vol=25% | $7.46 | $745.89 | $0.00 | $7.46 |
Put-call parity is the built-in audit: for the worked inputs, call minus put should equal S minus the discounted strike, 100 − 105·e−0.05×0.25 = −3.70, and 2.48 − 6.17 = −3.69 after rounding. It reconciles, which is how you know the two formulas are consistent with each other.
How the premium splits: worked call versus the same-strike put
What the two parts of a premium mean
Intrinsic value is money already in the option; time value is the price of possibility. An out-of-the-money option is pure possibility, and an option at expiry is pure intrinsic value.
Intrinsic value is the profit you would pocket by exercising right now: for the worked call with the stock at $100 and a $105 strike, that is max(0, 100 − 105) = $0.00, because nobody pays $105 for the right to buy something worth $100. The same-strike put has $5.00 of intrinsic value (105 − 100), money that is real the moment you hold it. Time value is everything else: the $2.48 on the worked call is entirely time value, the market's payment for three months of chances that the stock climbs past $105. Time value is largest for at-the-money options, where uncertainty peaks, and it decays to zero at expiry as those chances run out. A useful cross-check from professional trading: the time value of the same-strike call and put in the same expiry is nearly identical, and here $2.48 of call time value sits next to $1.17 of put time value only because the put carries $5.00 of intrinsic value the call does not.
The break-even follows directly: a call buyer profits only if the stock exceeds the strike plus the premium at expiry ($107.48 on the worked example), a put buyer only if it falls below the strike minus the premium ($98.83). Knowing the premium without knowing the break-even is knowing the price of a ticket without knowing the destination.
What competing calculators miss
The rival set splits into rich tools with narrow audiences and clear explainers with no tool at all:
- FinMBA's options pricer: the strongest tool of the set, with a stats bar showing premium, intrinsic value, time value and break-even plus scenario stress-testing. It is rupee-oriented, shows no contract total, and offers no copy or embed path, so a US retail trader still has to do the last multiplication by hand.
- CtrlCalculator's Black-Scholes calculator: the most auditable page, printing d1, d2, N(d1) and N(d2) in a strike ladder so you can check its arithmetic. The table is a static worked example rather than an interactive tool, so your own inputs never get the same transparency.
- Tradetron's premium guide: a genuinely clear intrinsic-plus-time-value explainer with worked NIFTY examples and video. A guide, not a calculator: no inputs, no outputs.
- Secure Put Calls' premium guide: the best statement of the 100-share contract reality (a $3.00 premium costs $300 before fees) and of why the seller's premium is not automatically profit. Again prose, not a tool.
- LegalClarity's option price explainer: careful on the intrinsic/time-value split with clean dollar examples. No calculator attached.
- Bajaj Finserv's option premium page: worked rupee examples plus an explicit Black-Scholes section naming time value, volatility and rates as the model's ingredients. Educational page, no interactive pricing.
- The gap this page fills: a live Black-Scholes pricer for both calls and puts that shows the per-option premium, the contract cash total, and the intrinsic/time-value split together, with a worked example whose every number reproduces in the tool above, put-call parity shown as the audit, and the European, no-dividend assumptions stated instead of hidden.
Frequently asked questions
The premium is the price of the option contract itself: what the buyer pays and the seller receives for the right, but not the obligation, to buy or sell the underlying at the strike price before expiry. It is quoted per share of the underlying, so a $2.48 premium on a standard 100-share contract costs the buyer $248.00 in cash. The buyer's maximum loss is that premium; the seller keeps it if the option expires worthless.
It values a European option as its discounted expected payoff, calculated through two intermediate values, d1 and d2, fed into the cumulative normal distribution. For a call, the formula is S times N(d1) minus the discounted strike K times N(d2); the put mirrors it. The inputs are the underlying price, strike, time to expiration, risk-free rate and volatility, and the model assumes constant volatility and rates, no dividends and no early exercise.
Intrinsic value is what the option would be worth if it expired right now: the immediate profit from exercising. For a call it is the stock price minus the strike, for a put the strike minus the stock price, and it is never negative. The worked call with the stock at $100 and a $105 strike has $0.00 of intrinsic value because it is out of the money; the same-strike put has $5.00.
Time value is the portion of the premium above intrinsic value: the market's payment for the chance that the option moves further into the money before expiry. It is largest for at-the-money options and decays to zero as expiration approaches, a process called time decay. An out-of-the-money option has zero intrinsic value, so its entire premium, $2.48 in the worked example, is time value.
Because the premium is quoted per share but contracts cover many shares: standard US equity options control 100 shares each. The multiplier turns the $2.48 per-option premium into the $247.79 one contract actually costs, which is the number that matters for position sizing and for comparing the premium against your account risk.
The Black-Scholes formula needs time as a year fraction because volatility and the risk-free rate are annualized: three months is 0.25, six months is 0.5, one year is 1. An earlier version of this page suggested days or months could be entered directly, which was wrong, since the formula would then mix annualized rates with day counts. Enter the decimal-year figure the label asks for.
No. The textbook Black-Scholes formula prices European options on non-dividend-paying underlyings with constant volatility, and that is what this tool implements. Most US-listed equity options are American-style and many stocks pay dividends, both of which raise or lower the true value versus the model. Treat the result as a fair-value estimate for comparison, not as a tradable quote.
In the model, no: the worst case is a worthless option priced at zero, because the right to buy or sell can simply go unexercised. If this tool ever returned a negative premium, that would signal a bug rather than a market insight. Real market quotes are also never negative, though deep out-of-the-money options can trade at a single cent.
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References
- U.S. Government Publishing Office. Federal Register, Volume 84, Issue 161: regulatory definitions of intrinsic value (the difference between the underlying price and the strike) and time value (premium minus intrinsic value), citing Natenberg's Option Volatility and Pricing. Accessed October 23, 2026.
- Bajaj Finserv. Options Premium: Meaning, Calculation and Formula: worked intrinsic and time value examples and the Black-Scholes model's role in estimating theoretical value. Accessed October 23, 2026.
- Tradetron. How to Calculate Option Premium (With Examples): premium as intrinsic value plus time value, with quoted-premium versus lot-size cash cost examples. Accessed October 23, 2026.
- Secure Put Calls. How to Calculate Option Premium: Complete Guide: intrinsic versus extrinsic value and the standard 100-share US equity contract multiplier. Accessed October 23, 2026.
- ExcelPriceFeed. Black-Scholes Option Pricing and Greeks Formulas: the Black-Scholes premium, delta, gamma, theta and vega formulas with parameter definitions. Accessed October 23, 2026.
- OptionsTrading.org. Black Scholes Pricing Model: history, purpose, inputs and assumptions of the model, including its 1973 publication. Accessed October 23, 2026.
- AdvisorHub. Understanding Options: standardized contract terms, the OCC guarantee, and the 100-share round lot convention. Accessed October 23, 2026.
- Netpicks. Easy To Understand Option Basics: in-the-money, at-the-money and out-of-the-money definitions and how volatility inflates option prices. Accessed October 23, 2026.
- Open Exam Prep. Options Basics, Series 7 Study Guide: moneyness, the premium equals intrinsic plus time value identity, and theta decay. Accessed October 23, 2026.
- IBIMA Publishing, Journal of Financial Studies and Research. Drawbacks and Limitations of Black-Scholes Model for Options Pricing: the model's ideal-market assumptions and extensions such as Merton's dividend adjustment. Accessed October 23, 2026.