An arithmetic grid bot spaces its price levels by a fixed amount; a geometric grid bot spaces them by a fixed percentage. Across the same range, arithmetic gaps become smaller in percentage terms as prices rise, while geometric gaps grow in currency terms. Neither spacing rule establishes profitability. Compare the complete submitted ladder, order sizes and fees before deciding whether either configuration fits your plan.
The useful question is what remains constant: the price difference or the price ratio. A second question follows immediately: constant for which quantity? Equal asset units and equal purchase budgets produce different cash results even when their price levels match.
This guide builds both ladders, checks every interval, and then applies fees and rounding. All prices, quantities, fees and trading rules below are hypothetical. They illustrate grid mathematics without claiming that KLINEO offers a grid bot.
Start with the same boundaries and interval count
Binance's Spot Grid explanation describes arithmetic grids as equal price differences and geometric grids as equal price ratios. The distinction also appears in OKX's futures-grid setup documentation. The common mathematics does not make their funding, order management or product rules interchangeable.
Use a fictional spot asset with a lower boundary of $80 and an upper boundary of $160. Divide that range into four intervals. Including both endpoints gives five price levels. Here, N always means the number of intervals; if another tool asks for the number of levels, translate the count before comparing outputs.
For arithmetic spacing, calculate the fixed difference:
d = (upper − lower) / N = (160 − 80) / 4 = $20
The level at index i is lower + i × d, for i from zero through four.
For geometric spacing, calculate the fixed ratio:
r = (upper / lower)^(1/N) = 2^(1/4) ≈ 1.189207115
The level at index i is lower × r^i. The percentage gap is (r − 1) × 100, approximately 18.9207%, rather than 118.9207%.
| Level index | Arithmetic price | Geometric price |
|---|---|---|
| 0, lower boundary | $80.00 | $80.0000 |
| 1 | $100.00 | $95.1366 |
| 2 | $120.00 | $113.1371 |
| 3 | $140.00 | $134.5434 |
| 4, upper boundary | $160.00 | $160.0000 |
Geometric prices are displayed to four decimals here. Calculations use the unrounded values. These five levels describe possible pair boundaries, not five orders that must all be open simultaneously; that depends on the bot's placement and inventory rules.
Compare every percentage spread
For an adjacent buy price b and sell price s, the gross spread relative to the buy price is (s / b − 1) × 100. Use the lower price as the denominator consistently.
| Interval | Arithmetic gap | Arithmetic gross spread | Geometric gap | Geometric gross spread |
|---|---|---|---|---|
| 0 → 1 | $20.00 | 25.0000% | $15.1366 | 18.9207% |
| 1 → 2 | $20.00 | 20.0000% | $18.0005 | 18.9207% |
| 2 → 3 | $20.00 | 16.6667% | $21.4063 | 18.9207% |
| 3 → 4 | $20.00 | 14.2857% | $25.4566 | 18.9207% |
The arithmetic ladder gives the same $20 gross gain for a completed one-unit pair, but buying that unit at $140 ties up more cash than buying it at $80. Its percentage spread therefore falls toward the top.
The geometric ladder keeps the ratio constant by increasing the dollar distance between higher levels. That is a proportional spacing rule, not evidence that prices will traverse those gaps or that every pair will fill.
Across a narrow relative range, the two ladders can look similar. Their difference becomes more visible as the ratio of upper to lower boundary grows. Choosing a mode still requires an explicit range and count: “geometric” alone does not tell you how far apart the orders are.
Order sizing changes the cash comparison
Suppose each completed pair buys and sells exactly one asset unit. Before fees, every arithmetic pair gains $20. The geometric pairs instead gain approximately $15.14, $18.00, $21.41 and $25.46.
Now imagine each pair uses a fixed $100 purchase notional, with fractional quantities allowed and fees ignored. Its quantity is 100 / buy price. Each geometric pair then has the same $18.9207 gross gain because the percentage spread is constant. Arithmetic pair gains become $25.00, $20.00, $16.67 and $14.29.
Both statements about a “constant gain per grid” can therefore be mathematically correct under different sizing assumptions. Ask whether the software holds base quantity, quote purchase value or another allocation measure constant. The spacing label does not answer that question.
These are isolated matched-pair calculations. They do not establish equal starting inventory, maximum capital use, turnover or final equity across complete bots. For the broader distinction between averaging cycles and paired orders, the DCA bot versus grid bot comparison follows cash and remaining holdings along one price path.
Deduct both transaction fees from the pair
Assume each example buys and later sells one full unit at the stated levels. A fee of 0.10% is charged in dollars on each transaction's notional. There are no other costs, quantity deductions or partial fills. This invented fee is not a current venue or account rate.
For quantity q and fee rates f_buy and f_sell:
Net pair cash = q × [s × (1 − f_sell) − b × (1 + f_buy)]
The sale fee uses the sale notional; the purchase fee uses the purchase notional. A single subtraction from the quoted price gap misses that distinction.
| One-unit completed pair | Gross gain | Combined fees | Net pair cash |
|---|---|---|---|
| Arithmetic, $80 → $100 | $20.00 | $0.1800 | $19.8200 |
| Arithmetic, $140 → $160 | $20.00 | $0.3000 | $19.7000 |
| Geometric, $80 → $95.1366 | $15.1366 | $0.1751 | $14.9614 |
| Geometric, $134.5434 → $160 | $25.4566 | $0.2945 | $25.1620 |
Even the arithmetic grid's dollar result stops being constant after these fees. The geometric grid retains a constant net percentage under the stated assumptions: divide sale proceeds after fees by purchase cost including fees, then subtract one. That gives approximately 18.6831% for each unrounded geometric pair. This denominator differs from purchase notional before fees, so label it in any report.
The large example gaps make fee effects easy to see, but do not imply useful trading settings. Consider a separate tight pair: buy at $100 and sell at $100.15. Its $0.15 gross gain becomes a $0.05015 cash loss after the same two 0.10% fees.
For positive pair cash under this quote-fee model, require s / b > (1 + f_buy) / (1 − f_sell). With both rates at 0.10%, the gross spread must exceed approximately 0.2002% before any other cost. Subtracting a flat 0.20% is only an approximation. Use the actual fee asset, quantity received and fill records when the model differs.
Rounding changes the geometric ladder
An exchange accepts prices on its permitted tick grid, not every real number produced by a formula. Binance Spot documents separate price ticks, quantity steps and notional constraints in its API filter specification. Those rules illustrate why mathematical levels need another validation stage; this example does not quote live symbol limits.
Suppose our fictional market allows prices in increments of $1. For illustration, round every geometric level to the nearest dollar. This is a hypothetical normalization policy, not a recommendation to round every order that way.
| Submitted pair after rounding | Gross spread |
|---|---|
| $80 → $95 | 18.7500% |
| $95 → $113 | 18.9474% |
| $113 → $135 | 19.4690% |
| $135 → $160 | 18.5185% |
The submitted ladder is no longer perfectly geometric. Recalculate its spreads and fees from these prices; retaining the original 18.9207% on a summary screen would describe the theoretical ladder instead of the normalized orders.
Rounding can also erase levels. A different arithmetic ladder from $100 to $101 with four intervals has theoretical prices of $100, $100.25, $100.50, $100.75 and $101. Rounding halves upward to a $1 tick yields $100, $100, $101, $101 and $101. There are only two distinct submitted prices. A four-interval strategy cannot be represented by that result.
Quantity normalization adds another constraint. A valid price does not establish a valid quantity or affordable order. Apply the size increment, then recompute notional and funds needed, including fees under the actual fee model. The exchange order minimums worksheet explains when no permitted quantity fits the budget.
Validate the ladder before evaluating the strategy
Use this worksheet with the actual venue, market and account rules. Keep both intended and submitted values so any normalization remains visible.
| Record | Validation question |
|---|---|
| Lower boundary, upper boundary and interval count | Are the endpoints ordered, positive and counted consistently? |
| Raw price levels | Does the final level reach the upper boundary with the intended difference or ratio? |
| Submitted price levels | Do all prices satisfy applicable filters and remain strictly increasing? |
| Quantity at each order | Which sizing measure is constant, and does rounding preserve the authorized budget? |
| Notional and available funds | Does every individual request pass, with funds reserved for concurrent orders and fees? |
| Adjacent pair economics | What remains after both fees using submitted prices and executable quantities? |
| Inventory and stop rules | What remains held if price leaves the range or the bot stops? |
| Execution evidence | Can a supported test establish placement, fill handling and replacement behavior? |
A price touching a level does not prove a full fill. A partial purchase can leave too little inventory for the intended sale; a rejected replacement can leave a missing pair. Check those cases before assuming the theoretical ladder will keep repeating.
Completed positive pairs can also coexist with a loss on unsold inventory. The grid profit versus total return ledger connects those numbers to account equity. For derivatives, add the contract, margin and funding rules described in futures grid funding and leverage; the spot cash model above does not cover them.
Choose arithmetic spacing when the rule you intend to express uses equal price differences, and geometric spacing when it uses equal ratios. Then inspect the normalized ladder. If prices collapse together, individual orders fail validation, or costs consume the intended pair spread, revise the configuration before treating it as an executable plan.