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Impermanent Loss Calculator With Rewards

Originally published · 4 min read · Updated

Calculate impermanent loss against holding, then add trading fees and rewards; the worked example shows the APR needed to break even.

TL;DR: If one asset in a 50/50 pool doubles, impermanent loss is 5.72%; rewards must cover that gap, gas, and any incentive-token decline.

impermanent lossliquidity poolsDeFi calculatorLP rewards
Table of contents

A liquidity-pool curve balanced against fee and reward tokens

When one asset in a constant-product 50/50 pool doubles relative to the other, the LP position trails a simple hold by 5.72% before fees and rewards.

Calculate impermanent loss with rewards

50/50 constant-product pool; fee and reward APR use simple interest on the starting deposit.

2 means one asset doubles relative to the other.
Price scenarios

Net versus holding

-$424.71

After fee income, reward income, and costs over 90 days.

Hold value
$15,000.00
LP before income
$14,142.14
Impermanent loss
-5.72%
IL dollar gap
-$857.86
Trading fee income
$0.00
Reward income
$493.15
Net LP value
$14,575.29
Break-even total APR
37.22%

The calculator compares the LP against holding the original 50/50 token amounts. For concentrated or weighted pools, use the advanced impermanent loss calculator.

Impermanent loss calculator formula

For a 50/50 constant-product pool, let r be the ending price divided by the starting price:

IL = 2 x sqrt(r) / (1 + r) - 1

Relative price changeImpermanent loss vs holding
1.25x-0.62%
1.50x-2.02%
2.00x-5.72%
3.00x-13.40%
0.50x-5.72%

The result is symmetric: a 2x move and a 50% move produce the same percentage gap. It is called impermanent because convergence can close the gap, not because the loss is imaginary. Withdrawing realizes the current difference versus holding.

This formula does not apply unchanged to concentrated liquidity, weighted pools, stableswap curves, or pools with multiple assets.

Impermanent loss calculator with rewards example

Start with $10,000 split equally between a stable asset and a volatile asset. The volatile asset doubles while the stable asset stays at $1.

  • Holding ends at $15,000.
  • The 50/50 LP ends at approximately $14,142.14 before earned fees.
  • The LP trails holding by $857.86.

Now add a 20% reward APR for 90 days, calculated on the original $10,000:

reward = $10,000 x 20% x 90 / 365 = $493.15

If entry, harvest, and exit cost $60, the comparison becomes:

$14,142.14 + $493.15 - $60 - $15,000 = -$424.71

The position earned a high headline APR and still lost $424.71 relative to holding. That benchmark matters: a positive dollar balance is not proof that LPing was the better action.

LP rewards needed to offset impermanent loss

For the same 90-day example, the reward needed to cover the $857.86 gap plus $60 of costs is $917.86. On $10,000 of starting capital:

break-even APR = $917.86 / $10,000 x 365 / 90 = 37.22%

That is a total reward APR, not an advertised token emission rate. Discount rewards for:

  • incentive-token price decline before sale;
  • vesting or claim delay;
  • gas and swap costs;
  • reward dilution as TVL grows;
  • taxes where applicable.

Value unreleased points at $0 in the base case. Adding a speculative points value can make any pool look profitable on paper.

Impermanent loss with concentrated liquidity

Concentrated liquidity needs the position's lower tick, upper tick, entry price, current price, unclaimed fees, and token amounts. When price leaves the range, the position becomes entirely one asset and stops earning in-range fees.

A narrow range can quote a large fee APR because the same capital supplies more local liquidity. It also converts faster into the underperforming asset. The relevant comparison is:

LP ending value + fees + sold rewards - gas versus value of the original token amounts held

Do not feed a concentrated position into a 50/50 full-range calculator and call the result risk-adjusted.

How to use an impermanent loss rewards calculator

  1. Enter the relative price change, not the portfolio's dollar return.
  2. Use the value of the assets you would otherwise hold as the benchmark.
  3. Add fees actually earned, not the pool's trailing APR applied blindly.
  4. Mark incentive tokens at executable sale price after vesting.
  5. Subtract entry, harvest, rebalance, hedge, and exit costs.
  6. Run at least 0.5x, 1.5x, 2x, and out-of-range scenarios.

Our opinion: fee APR is only credible when paired with the volume period, active liquidity, and price range. A single annualized number can turn one abnormal day into a fictional year.

For the rest of the risk stack, see yield farming risks.

Sources

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