Three way matching is the comparison of three documents before an invoice is paid: what was ordered, what arrived, and what is being billed. It is the central routine control of accounts payable, it is cheap when all three exist, and it cannot run at all when any of them is missing, which turns out to be the main thing to understand about it.
The three documents
The purchase order records what was agreed with the supplier. 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 own organisation, which is why the quality of this control is mostly within your gift.
What agreement means
Supplier, unit price, quantity and total, compared at line level, within a tolerance. Tolerance exists because real invoices differ from real orders constantly: rounding, freight added at billing, part deliveries. A percentage with an absolute cap is the usual shape, reviewed after a month against the exceptions it actually produced.
What it prevents
Paying for goods that never arrived, which only the receipt can catch. 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.
Why it usually fails
Through absence rather than disagreement. No order raised, or no receipt recorded. Both are generated outside payables, by buying without an order and by deliveries nobody registers. Counting exceptions by reason usually puts these two at the top, which points improvement upstream rather than at the matching engine.
Questions people ask about what is 3 way matching
What is two way matching?
Invoice against order only, without the receipt. Correct for services and anything without a physical delivery; for goods it removes the check that they arrived.
Who performs the match?
Usually software, with a person handling what fails. The value of automating it is consistency rather than speed.
How do we improve the clean match rate?
Raise purchase-order coverage and record receipts promptly. Both are upstream and neither is a software setting.