---
title: "Impermanent loss for a 50/50 constant-product LP position vs simply holding, given the price change of the volatile asset."
method: POST
path: "/v1/crypto/impermanent-loss"
tags: ["Crypto & DeFi"]
---

# Impermanent loss for a 50/50 constant-product LP position vs simply holding, given the price change of the volatile asset.

`POST /v1/crypto/impermanent-loss`

## Request

- Base URL: `` (relative, and it does not resolve against the document’s source URL)
- URL: `/v1/crypto/impermanent-loss`
- Auth: none declared

Impermanent loss for a 50/50 constant-product LP position vs simply holding, given the price change of the volatile asset.

Payment: x402 ($0.05 USDC on eip155:8453). Call unpaid to receive an HTTP 402 with requirements, then retry with the PAYMENT-SIGNATURE header. Method: IL_fraction = 2*sqrt(r)/(1+r) - 1, r = currentPrice/initialPrice; dollar loss = -IL_fraction * positionValue

## Request body

- object
  - `initialPrice` number, required
  - `currentPrice` number, required
  - `positionValueUsd` number

## Response `200`

Verified result + provenance (formula, sources, reproducible SHA-256 hash).

## Other responses

- `400`: Invalid input (no charge) — body echoes the JSON Schema.
- `402`: Payment required — PAYMENT-REQUIRED header carries the x402 accepts[] quote.

---

[API](https://skmtc.dev/x402toll/apis/tollbooth-verified-calculators-for-ai-agents.md) · [All operations](https://skmtc.dev/x402toll/apis/tollbooth-verified-calculators-for-ai-agents/llms.txt) · [OpenAPI document](https://skmtc.dev/x402toll/apis/tollbooth-verified-calculators-for-ai-agents/revisions/60cb70a3e1a5?raw)