APR ↔ APY Converter
Convert APR (nominal annual rate) to APY (effective annual yield) for any compounding frequency including continuous — the exact DeFi math that decides whether a 10% APR pool really pays 10%. Deterministic closed-form, no approximations.
Worked examples
10% APR, monthly compounding
GET /api/v1/crypto/apr-apy?ratePct=10&compounding=monthly
Result: 10% APR = 10.47% APY (monthly)
5% APR, daily compounding
GET /api/v1/crypto/apr-apy?ratePct=5&compounding=daily
Result: 5% APR = 5.13% APY (daily)
12% APR, continuous
GET /api/v1/crypto/apr-apy?ratePct=12&compounding=continuous
Result: 12% APR = 12.75% APY (continuous)
Machine API (x402)
$0.002 / callThis tool is also a JSON API for AI agents. Requests without payment receive 402 Payment Required plus instructions; agents pay USDC on Base via the x402 protocol — no accounts, no API keys.
GET /api/v1/crypto/apr-apy?ratePct=10&compounding=monthly HTTP/1.1
Host: agentstoolshub.com
→ 402 (payment required, instructions in headers)
→ 200 (after X-PAYMENT header; JSON body below)
{
"tool": "crypto/apr-apy",
"input": {"ratePct":10,"compounding":"monthly"},
"result": { "value": 10.47, "answer": "10% APR = 10.47% APY (monthly)" }
}Agent docs: /llms.txt · OpenAPI spec · integration guide
About this tool
Exact APR→APY conversion across annual, quarterly, monthly, daily and continuous compounding. This is the math behind every staking and yield display: a 10% APR compounds to 10.47% APY monthly, 10.52% daily, 10.52% continuous. Deterministic, so quoting it never drifts.
APY = (1 + APR/n)^n − 1; continuous: APY = e^APR − 1
Frequently asked questions
Why is APY always higher than APR?
APY counts interest-on-interest within the year; APR is the simple nominal rate. They converge as compounding becomes annual.
Which do DeFi protocols quote?
Both, inconsistently — staking UIs usually show APY, lending markets APR. This tool is the bridge; always compare like with like.