# Futures Basis and Forward Price Calculator > Free futures basis calculator. Enter spot and futures prices, days to expiry, interest rate and yield to get the basis, cost of carry fair value and implied rate. Source: https://learn.tradelabsai.com/tools/futures-basis-calculator/ Track: Calculators · Level: Beginner · Updated: 2026-10-03 Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice. Cite as: TradeLabs Learn, "Futures Basis and Forward Price Calculator", https://learn.tradelabsai.com/tools/futures-basis-calculator/ A futures price is rarely equal to the spot price. The difference, called the basis, reflects the cost of carrying the asset until expiry: interest on the money tied up, minus any income the asset pays, plus storage for physical commodities. This calculator compares a futures price with its theoretical cost of carry fair value and shows the annualised rate the market is implying. It is useful for index futures, crypto futures and any market where you want to know whether futures look rich or cheap relative to spot. ## Calculator *Interactive calculator: use it at https://learn.tradelabsai.com/tools/futures-basis-calculator/* ## How it works ``` Basis = Futures price - Spot price Fair value = Spot × e^((r - y) × T) Implied carry rate = ln(Futures / Spot) / T + y Annualised basis = (Futures / Spot - 1) / T ``` T is time in years (days divided by 365). For commodities, storage costs add to r. Note that in commodity markets, basis is often defined the other way round, as spot minus futures; this calculator uses futures minus spot. See [Basis and Basis Trading](https://learn.tradelabsai.com/futures/basis-and-basis-trading/). **Example: An index future** A stock index trades at 5,000 and its 90 day future at 5,050, a basis of 50 points. With a 5% interest rate and a 1.5% dividend yield, the fair value is 5,000 times e to the power of 3.5% times 90 divided by 365, about 5,043.3. The future trades about 6.7 points above fair value. The implied carry rate is about 5.5% a year versus the 5% interest rate, so the future looks slightly rich. Before concluding there is an arbitrage, a trader would include transaction costs, financing spreads and the exact dividend schedule. See [Cash-and-Carry Arbitrage](https://learn.tradelabsai.com/futures/cash-and-carry-arbitrage/). ## Contango and backwardation | State | Futures versus spot | Typical cause | |---|---|---| | Contango | Futures above spot | Positive carry: interest and storage exceed income. See [Contango](https://learn.tradelabsai.com/futures/contango/) | | Backwardation | Futures below spot | High income, scarce supply or strong demand for the physical asset now. See [Backwardation](https://learn.tradelabsai.com/futures/backwardation/) | ## Crypto basis In crypto, the basis on dated futures and the funding rate on perpetual futures can be far higher than interest rates, especially in bull markets when traders pay up for leverage. A trader can buy spot and sell futures to earn the basis, a trade often called a cash and carry or basis trade, while facing exchange, counterparty and margin risks. Enter a crypto future here with a zero income yield to see its implied annual rate. See [Crypto Futures and Basis](https://learn.tradelabsai.com/crypto/crypto-futures-and-basis/) and [Funding and Basis Arbitrage](https://learn.tradelabsai.com/crypto/funding-and-basis-arbitrage/). ## Convergence at expiry As expiry approaches, the basis shrinks toward zero, because the futures price must converge to spot at settlement. Basis traders profit from that convergence; hedgers face basis risk if they close a hedge before expiry or hedge one asset with another's futures. See [Hedging](https://learn.tradelabsai.com/markets/hedging/) and [Settlement](https://learn.tradelabsai.com/markets/settlement/). ## Common mistakes 1. **Ignoring dividends or income,** which lowers fair value. 2. **Using the wrong rate:** your actual borrowing cost may be above the risk free rate. 3. **Forgetting costs,** which can erase small mispricings. 4. **Comparing different times:** spot and futures prices must be taken at the same moment. 5. **Mixing basis conventions** between markets. ## Tracking the basis over time Record the basis daily for the contract you trade; sudden changes often signal shifts in funding demand or positioning. ## Frequently asked questions ### What is futures basis? The difference between the futures price and the spot price, reflecting financing costs, income and storage until expiry. ### How is fair value of a futures contract calculated? Spot price times e raised to the interest rate minus the income yield, times the time to expiry in years. ### Why do futures trade above spot? Usually because holding the asset has a net cost, mainly interest, which the futures price includes; this is called contango. Next, calculate currency forward rates with the [FX Forward Points Calculator](https://learn.tradelabsai.com/tools/fx-forward-points-calculator/). ## Continue learning - Next lesson: [FX Forward Points Calculator](https://learn.tradelabsai.com/tools/fx-forward-points-calculator/) - Previous lesson: [Binomial Option Pricing Calculator](https://learn.tradelabsai.com/tools/binomial-calculator/) - Related: [Binomial Option Pricing Calculator](https://learn.tradelabsai.com/tools/binomial-calculator/): Free binomial option pricing calculator using a Cox Ross Rubinstein tree. Price American or European calls and puts and see the early exercise premium. - Related: [Basis and Basis Trading](https://learn.tradelabsai.com/futures/basis-and-basis-trading/): Basis is the gap between a spot price and a futures price. Learn how hedgers manage basis risk, how basis trades work and the Treasury basis trade. - Related: [Cash-and-Carry Arbitrage](https://learn.tradelabsai.com/futures/cash-and-carry-arbitrage/): Cash and carry arbitrage buys an asset and sells its futures when futures are rich versus carry costs. Learn the formula, gold, index and crypto examples, and risks. - Related: [Contango](https://learn.tradelabsai.com/futures/contango/): Contango is when later futures trade above nearer ones or spot. Learn why it happens, how it erodes long commodity and VIX funds, and how traders use it. - Related: [Backwardation](https://learn.tradelabsai.com/futures/backwardation/): Backwardation is when later futures trade below nearer ones or spot. Learn the causes, convenience yield, positive roll yield and what it signals about supply. - Related: [Crypto Futures and Basis](https://learn.tradelabsai.com/crypto/crypto-futures-and-basis/): Dated crypto futures trade at a premium or discount to spot called the basis. Learn CME and exchange futures, how to annualise basis and what it tells traders.