Three way matching in accounts payable is the comparison of three documents before an invoice is paid: what was ordered, what arrived, and what is being billed. When all three agree within tolerance the invoice can be paid with confidence. When they do not, the disagreement is the point, because it names a specific problem that somebody can resolve.
The three documents
The purchase order records what was agreed with the supplier: item, quantity and price. The goods receipt records what actually arrived and when, made by whoever took the delivery. The invoice is the supplier's claim for payment. Two of the three are produced inside your organisation, which is why their quality is your responsibility rather than the supplier's.
What it protects against
Paying for goods that never arrived, which only the receipt can prevent. Paying a price nobody agreed, which only the order can catch. And paying twice for one delivery, which line-level matching with running quantities prevents. No other routine check in payables covers those three, which is the real argument for the upstream effort it requires.
Tolerance, and why it exists
Real invoices differ from real orders in small ways constantly: rounding, freight added at billing, part deliveries. Tolerance is the size of difference allowed to pass without a person looking. Set it as a percentage with an absolute cap, and review it after a month against the exceptions it actually produced rather than leaving a default in place.
Questions people ask about what is three way matching in accounts payable
What is two way matching?
Invoice against order only, without the receipt. It is correct for services and anything without a physical delivery, and it removes the protection against paying for undelivered goods.
Who performs the match?
Usually software, and a person handles what fails. The value of automation here is consistency rather than speed.
What if there is no purchase order?
The match cannot run, and the invoice must be approved on its own merits by whoever authorised the spend. That path is many times more expensive.