How to Use an Arbitrage Calculator

Every sports arbitrage bet comes down to one question: do the odds across two or more bookmakers add up to less than 100%? If they do, you have a sure bet, a guaranteed profit regardless of the outcome. An arbitrage betting calculator is the tool that answers that question and tells you exactly how much to stake on each side.

In this guide, we'll break down the exact formulas behind an arb calculator, walk through real examples with actual numbers, and show you how to go from spotting an opportunity to calculating your guaranteed profit in seconds.

What Is an Arbitrage Betting Calculator?

An arbitrage calculator (also called a sure bet calculator or arb calculator) is a tool that does three things:

1. Detects whether an arbitrage opportunity exists between two or more odds
2. Calculates the exact stake for each outcome to guarantee equal profit
3. Shows your guaranteed profit percentage and dollar return

The free calculator above goes beyond basic arb detection. It includes three modes: Standard Arb (2-way and 3-way), Middle Finder (detects spread/total overlaps where both sides can win), and Asian Handicap (handles half lines, whole lines with push, and quarter lines with split stakes). It supports all four major odds formats: decimal, American, fractional, and probability (for Kalshi/Polymarket prices).

You can also build a basic version in a spreadsheet, or, if you're serious about arbing, use software like Claw Arbs that runs these calculations automatically across thousands of markets in real-time.

But before you rely on any tool, you need to understand the math yourself. Knowing how to calculate arbitrage by hand lets you verify opportunities, understand edge sizes, and make better decisions when conditions change mid-trade.

The Core Formula: How to Detect a Sure Bet

The foundation of every arbitrage calculator is the arbitrage percentage (also called the overround or margin). Here's the formula for a two-outcome market:

Arb % = (1 / Odds A) + (1 / Odds B)

If the arb percentage is less than 1.00 (or 100%), an arbitrage opportunity exists. The lower the number, the bigger the edge.

Example: Detecting an Arb

Say you're looking at an NBA game, Lakers vs Celtics. You find these decimal odds:

Outcome	Sportsbook	Decimal Odds
Lakers to win	Pinnacle	2.15
Celtics to win	DraftKings	1.95

Plug into the formula:

Arb % = (1 / 2.15) + (1 / 1.95) = 0.4651 + 0.5128 = 0.9779

That's 97.79%, below 100%, so this is a sure bet. Your guaranteed profit margin is 1 - 0.9779 = 0.0221, or 2.21%.

What If There's No Arb?

If the same game had odds of 1.90 and 1.90:

Arb % = (1 / 1.90) + (1 / 1.90) = 0.5263 + 0.5263 = 1.0526

That's 105.26%, above 100%. No arbitrage opportunity. The 5.26% above 100% is the combined bookmaker margin (the overround). You'd be paying the bookmakers' edge, not exploiting one.

How to Calculate Your Stakes

Once you've confirmed an arb exists, the next step is calculating exactly how much to bet on each outcome. The goal: equal profit regardless of which outcome wins.

The Stake Formula

For a total bankroll of B that you want to deploy on this arb:

Stake on Outcome A = B × (1 / Odds A) / Arb %
Stake on Outcome B = B × (1 / Odds B) / Arb %

Full Worked Example

Using our Lakers vs Celtics arb with a $1,000 total stake:

• Odds A (Lakers, Pinnacle): 2.15
• Odds B (Celtics, DraftKings): 1.95
• Arb %: 0.9779
• Total stake: $1,000

Stake on Lakers:

$1,000 × (1 / 2.15) / 0.9779 = $1,000 × 0.4651 / 0.9779 = $475.67

Stake on Celtics:

$1,000 × (1 / 1.95) / 0.9779 = $1,000 × 0.5128 / 0.9779 = $524.33

Now let's verify the profit for each outcome:

If Lakers Win	If Celtics Win
Payout: $475.67 × 2.15 = $1,022.69	Payout: $524.33 × 1.95 = $1,022.44
Profit: $1,022.69 - $1,000 = $22.69	Profit: $1,022.44 - $1,000 = $22.44

Guaranteed profit of approximately $22.50 on a $1,000 investment, no matter who wins. That's the 2.21% edge in dollar terms. The tiny difference between the two outcomes ($0.25) is due to rounding. In practice, you'd round stakes to whole dollars.

Arbitrage Calculator for Prediction Markets

If you're arbing between Kalshi and Polymarket, the math is slightly different because these platforms use probability-based pricing instead of decimal odds.

Converting Prediction Market Prices to Decimal Odds

Kalshi prices contracts in cents (e.g., buy YES at 45¢). Polymarket prices in decimals (e.g., 0.45). To convert to decimal odds:

Decimal Odds = 1 / Price

Examples:

• Kalshi YES at 45¢ → 1 / 0.45 = 2.222 decimal odds
• Polymarket NO at 0.52 → 1 / 0.52 = 1.923 decimal odds

Prediction Market Arb Example

Consider a political event where both platforms offer a contract:

Platform	Position	Price	Decimal Odds
Kalshi	YES	42¢	2.381
Polymarket	NO	0.55	1.818

Arb % = (1 / 2.381) + (1 / 1.818) = 0.42 + 0.55 = 0.97

That's 97%, a 3% edge. For $1,000 total:

• Kalshi YES stake: $1,000 × 0.42 / 0.97 = $432.99
• Polymarket NO stake: $1,000 × 0.55 / 0.97 = $567.01
• Guaranteed profit: ~$30

The key difference with prediction markets: you also need to factor in fees. Kalshi charges a fee tier (typically 7% for new accounts, decreasing with volume) on profits, and Polymarket has gas costs on the Polygon network. Always subtract these from your edge to get the true profit.

Accounting for Fees and Slippage

A raw arb percentage doesn't tell the whole story. Real-world profits are reduced by:

1. Exchange/Platform Fees

Kalshi charges a percentage fee on winning trades. If your Kalshi fee tier is 7% and you win $100 on a YES contract, you keep $93. Your arb calculator must account for this:

Effective Odds (Kalshi) = 1 + (Decimal Odds - 1) × (1 - Fee Rate)

For Kalshi YES at 42¢ (2.381 odds) with 7% fee:

Effective Odds = 1 + (2.381 - 1) × 0.93 = 1 + 1.284 = 2.284

Now recalculate the arb percentage with effective odds. This is why many arbs that look profitable at first glance disappear after fees.

2. Slippage

Slippage occurs when the price moves between the time you see the opportunity and the time your order fills. In fast-moving markets, the odds you calculated against may no longer be available. Professional arbers build a slippage buffer (typically 0.5-1%) into their calculations.

3. Minimum Edge Threshold

After accounting for fees and slippage, most serious arbers set a minimum edge threshold: the smallest arb percentage they'll act on. Common thresholds:

Strategy	Minimum Edge	Why
Manual arbing	2-3%	Need buffer for execution time
Semi-automated	1-2%	Faster execution, less slippage risk
Fully automated	0.5-1%	Sub-second execution, high volume

Claw Arbs lets you configure your minimum edge threshold, fee rates, and slippage buffer so that the calculator only surfaces opportunities with real, after-cost profit.

Three-Way Arb Calculator

Some markets have three outcomes (win/draw/lose in soccer, for instance). The formula extends naturally:

Arb % = (1 / Odds A) + (1 / Odds B) + (1 / Odds C)

Soccer Example

Manchester United vs Arsenal, with a draw possible:

Outcome	Book	Odds
Man Utd win	bet365	3.40
Draw	Pinnacle	3.60
Arsenal win	BetMGM	2.30

Arb % = (1/3.40) + (1/3.60) + (1/2.30) = 0.2941 + 0.2778 + 0.4348 = 1.0067

That's 100.67%, no arb here. But if BetMGM moved Arsenal's odds to 2.40:

Arb % = 0.2941 + 0.2778 + (1/2.40) = 0.2941 + 0.2778 + 0.4167 = 0.9886

Now it's 98.86%, a 1.14% edge. Three-way arbs are rarer but often have larger edges because three bookmakers need to disagree, and the third outcome (the draw) is harder to price efficiently.

Middle Bet Calculator: When Both Sides Win

A middle bet (also called a middle or middling) is a special type of arbitrage where you bet on both sides of a spread or total, and the lines at different bookmakers create a gap where both bets can win.

How Middles Work

Say you find these spreads on an NFL game:

Sportsbook	Bet	Odds
Pinnacle	Chiefs -3.5	1.91
DraftKings	Ravens +4.5	1.91

The gap between -3.5 and +4.5 is 1 point. If the Chiefs win by exactly 4, both bets win. You hit the middle. In all other outcomes, one side wins and one loses (or you have a standard arb if the combined odds allow it).

Middle exists when: Line A + Line B > 0

In this example: -3.5 + 4.5 = 1.0 > 0, so a middle exists. The wider the gap, the more likely you are to hit it. Use the middle finder calculator above to check any spread combination.

Middle vs Standard Arb

	Standard Arb	Middle Bet
Guarantee	Profit on every outcome	Profit only if middle hits; may lose small amount otherwise
Upside	Fixed (typically 1-3%)	Much higher when middle hits (can be 10-20x the stake risk)
Frequency	Common across moneylines	Requires spread/total disagreements

The best middle opportunities combine a standard arb (guaranteed profit regardless) with a middle gap (bonus profit if the score lands in the gap). These are called arb + middle and are the most profitable scenarios in sports betting.

Asian Handicap Arb Calculator

Asian handicap (AH) betting eliminates the draw by applying a handicap to one team. It's popular in soccer and creates unique arbitrage opportunities because of its three line types:

Half Lines (e.g., -0.5, -1.5, -2.5)

These work exactly like standard 2-way arbs. No push is possible, so one side always wins. Calculate the same way: Arb% = (1/Odds_Home) + (1/Odds_Away).

Whole Lines (e.g., -1, -2, -3)

With whole number handicaps, a push is possible. If the margin equals exactly the handicap, both stakes are refunded. This creates three outcomes instead of two:

• Home covers: Home bet wins, away bet loses
• Push: Both stakes returned (no profit, no loss)
• Away covers: Away bet wins, home bet loses

The push scenario makes whole-line AH arbs safer than they appear. Your worst case on a "losing" arb is getting your money back, not actually losing it.

Quarter Lines (e.g., -0.75, -1.25, -1.75)

Quarter lines are the most complex. Your stake is split 50/50 between two adjacent half-lines. For example, AH -0.75 splits into:

• Half on AH -0.5
• Half on AH -1.0

If the result falls between the two lines, you win one half and push the other. This partial-refund mechanism creates scenarios where the effective odds differ from the quoted odds, opening up arb opportunities that simple calculators miss. Use the Asian handicap calculator above to handle these automatically.

Why Asian Handicaps Create More Arbs

Asian handicap markets are priced independently from moneyline and standard spread markets. When a bookmaker adjusts their AH line but is slow to update their moneyline, a temporary edge opens up. Sharp bettors and automated tools like Claw Arbs monitor these cross-market discrepancies in real-time.

No-Vig Calculator: Find True Odds and Value Bets

Every bookmaker builds a margin (vig/juice) into their odds. The no-vig calculator strips this margin to reveal the true probability and fair odds for each outcome. This is the foundation of value betting. If a bookmaker offers odds higher than the fair price, you have a positive expected value bet.

How No-Vig Calculation Works

The formula is simple. For each outcome, divide its implied probability by the total implied probability (the overround):

True Probability = (1 / Offered Odds) / Sum of All Implied Probabilities

Example: Removing the Vig

A bookmaker offers a tennis match at:

Outcome	Odds	Implied %	True %	Fair Odds
Player A	1.91	52.4%	50.0%	2.000
Player B	1.91	52.4%	50.0%	2.000
Total		104.7%	100.0%

The bookmaker's margin is 4.7%. The true (fair) odds are 2.000 for each side. If another bookmaker offers Player A at 2.10, that's +5% value over the fair price, a positive expected value bet.

Using No-Vig for Value Betting

The typical workflow for value bettors:

1. Get the sharp line. Use a sharp bookmaker like Pinnacle as your reference. Their low-margin odds are the closest to true probability.
2. Remove the vig. Calculate the no-vig odds using the calculator above. This gives you the "true" price.
3. Compare against soft books. Enter a second bookmaker's odds in the "Book 2" fields. If their odds exceed the fair price, you have value.
4. Bet the value. Over hundreds of bets, positive EV compounds into consistent profit.

This is exactly how Claw Arbs works in cross-book mode. It uses sharp bookmaker lines (Pinnacle/PS3838) as the true price and flags when soft venues (Kalshi, Polymarket, retail sportsbooks) offer odds above the no-vig fair value.

How to Convert Between Odds Formats

Different sportsbooks use different odds formats. Your arb calculator needs to work with all of them. Here are the conversions:

American to Decimal

• Positive American (e.g., +150): Decimal = (American / 100) + 1 = 2.50
• Negative American (e.g., -200): Decimal = (100 / |American|) + 1 = 1.50

Fractional to Decimal

Decimal = (Numerator / Denominator) + 1

Example: 5/2 → (5/2) + 1 = 3.50

Decimal to Implied Probability

Probability = 1 / Decimal Odds

Example: 2.50 → 1 / 2.50 = 0.40 = 40%

When you're comparing Pinnacle (decimal odds) against Kalshi (cents-based probability), you're essentially comparing the same thing in different formats. Convert everything to implied probability, and if the probabilities across all outcomes sum to less than 1.00, you have your arb.

Building Your Own Arb Calculator in a Spreadsheet

You can build a functional arbitrage calculator in Google Sheets or Excel in five minutes. Here's the layout:

Cell	Label	Formula
B1	Odds A	(input)
B2	Odds B	(input)
B3	Total Stake	(input)
B4	Arb %	=(1/B1)+(1/B2)
B5	Is Arb?	=IF(B4<1,"YES","NO")
B6	Profit %	=(1-B4)*100
B7	Stake A	=B3*(1/B1)/B4
B8	Stake B	=B3*(1/B2)/B4
B9	Profit $	=B7*B1-B3

This gives you a working sure bet calculator. Plug in any two decimal odds and a stake amount, and it instantly tells you whether an arb exists and how to size your bets.

That said, a spreadsheet is a learning tool, not a trading tool. Real arb opportunities last seconds, not minutes. By the time you manually check odds, type them into a spreadsheet, and place your bets, the arb has likely closed. This is why automated tools like Claw Arbs exist. They run the calculator across every market in real-time and execute before the opportunity disappears.

Common Calculation Mistakes

Even experienced arbers make these errors:

• Forgetting to account for fees. A 1.5% arb with a 2% fee structure means you're losing money, not making it
• Mixing odds formats. Using American odds in a formula that expects decimal odds will give wildly wrong results
• Ignoring the overround. Comparing odds from the same bookmaker won't produce arbs because single-book odds always sum to >100%
• Not rounding stakes correctly. Betting $473.82 at a sportsbook flags your account as an arber. Round to $475 or $470 and accept the minor profit reduction. Read our guide on making money with arbitrage for more tips on staying under the radar
• Using stale odds. Calculating an arb on odds that have already moved is the fastest way to get a one-sided (naked) position instead of a hedged arb

From Calculator to Execution

Understanding the arbitrage calculator formula is step one. Here's the full pipeline from detection to profit:

1. Scan: compare odds across multiple bookmakers and prediction markets simultaneously
2. Calculate: run the arb formula, subtract fees, check against your minimum edge threshold
3. Size: compute optimal stakes for each leg using the stake formula
4. Execute: place both bets as fast as possible (leg 1, then leg 2)
5. Verify: confirm both orders filled at the expected prices. If one leg fails, you're exposed, so either hedge at a worse price or manage the naked position

Steps 1 through 4 need to happen in seconds, not minutes. That's the difference between a calculator (useful for learning) and a full arb detection and execution system (useful for actually making money).

The Bottom Line

The arbitrage betting calculator is the mathematical backbone of every sure bet. The formula is simple: convert odds to implied probabilities, check if they sum to less than 100%, and use the stake formula to split your bankroll for guaranteed profit.

What's not simple is doing this fast enough, across enough markets, to consistently profit. The arb calculator handles the math. Speed, scale, and execution are what separate the hobbyist from the professional arber, especially when it comes to live in-play arbitrage, where odds shift every second and manual calculations are impossible.

Learn the formulas. Build the spreadsheet. Then graduate to automated tools that run the same calculations across thousands of markets per second. That's how you turn a sure bet calculator into a sure bet income stream. For a comparison of tools that automate this entire pipeline, see our guide to the best arbitrage betting software in 2026.

Frequently Asked Questions

How do you calculate an arbitrage bet?

Calculate the arbitrage percentage by adding the inverse of each decimal odd: Arb% = (1/Odds_A) + (1/Odds_B). If the result is less than 1.00 (100%), a sure bet exists. Your guaranteed profit margin is (1 - Arb%). For example, odds of 2.15 and 1.95 give Arb% = 0.9779, meaning a 2.21% guaranteed profit.

How do you calculate stakes for a sure bet?

Use the formula: Stake_A = Total × (1/Odds_A) / Arb%. For a $1,000 arb with odds 2.15 and 1.95 (Arb% = 0.9779): Stake on Outcome A = $475.67, Stake on Outcome B = $524.33. This guarantees ~$22.50 profit regardless of outcome. Use the free calculator above to compute this instantly.

What is a good arbitrage percentage?

It depends on your execution speed. Manual arbers need 2-3% minimum edge to cover execution time and slippage. Semi-automated systems can profit from 1-2% edges. Fully automated tools like Claw Arbs can profitably capture edges as small as 0.5-1% because they execute in milliseconds. Always subtract platform fees before evaluating the edge.

Can you arbitrage Kalshi and Polymarket?

Yes. Convert prediction market prices to decimal odds (Decimal Odds = 1/Price), then apply the standard arb formula. For example, Kalshi YES at 42¢ (2.381 odds) and Polymarket NO at 0.55 (1.818 odds) gives Arb% = 0.97, a 3% edge. Factor in Kalshi's fee tier and Polymarket gas costs to get true profit. Read our Kalshi vs Polymarket arbitrage guide for a deep dive.

How do you calculate a 3-way arbitrage bet?

Extend the formula to three outcomes: Arb% = (1/Odds_A) + (1/Odds_B) + (1/Odds_C). If the sum is below 1.00, an arb exists. Three-way arbs are common in soccer (win/draw/lose). They're rarer than two-way arbs but often carry larger edges because the draw outcome is harder for bookmakers to price efficiently.

What is a middle bet in sports betting?

A middle bet is when you bet both sides of a spread at different bookmakers where the lines create a gap. For example, Chiefs -3.5 at one book and Ravens +4.5 at another. If the Chiefs win by exactly 4, both bets win. A middle exists when the sum of the two lines is greater than zero. The wider the gap, the higher the chance of hitting the middle. Use the middle finder calculator above to check any spread combination.

How do Asian handicap arbs work?

Asian handicap (AH) betting eliminates the draw by applying a handicap. There are three line types: half lines (-0.5, -1.5) work like standard 2-way arbs; whole lines (-1, -2) allow a push where stakes are refunded; quarter lines (-0.75, -1.25) split your stake 50/50 between two adjacent lines, creating partial-refund scenarios. AH markets are priced independently from moneylines, so cross-market discrepancies frequently create arb opportunities. Try the Asian handicap calculator above to analyze any line.

What are no-vig odds and how do you calculate them?

No-vig (no-vigorish) odds remove the bookmaker's margin to show the true probability. Calculate by dividing each outcome's implied probability by the total overround: True Probability = (1/Odds) / Sum of All Implied Probabilities. For example, odds of 1.91/1.91 have a 4.7% margin. The true fair odds are 2.000/2.000. If another bookmaker offers higher than the fair odds, you have a positive expected value (value) bet. Use the no-vig calculator above to strip margins from any bookmaker's odds and compare against a second book.