How seats are calculated: the Sainte-Laguë method, with a worked example
New Zealand turns party votes into seats with the Sainte-Laguë formula. Here's how it works, step by step, with a simple worked example and the real 2023 numbers.
In this guide
Once the party votes are counted, someone has to turn percentages into whole seats. You can't give a party 14.4 MPs. New Zealand uses a formula called the Sainte-Laguë method, named after the French mathematician André Sainte-Laguë. It's the same formula our seat builder and live results use.
Quick answer
- Only parties with 5% or an electorate seat take part.
- Each party's votes are divided by 1, 3, 5, 7, 9 and so on.
- The 120 largest results each win a seat.
- The method is designed to be fair to both big and small parties.
The method in five steps
- Take the qualifying parties. Those with at least 5% of the party vote or at least one electorate.
- Divide each party's votes by 1, 3, 5, 7, 9... This makes a list of numbers, called quotients, for each party.
- Put every quotient from every party into one list and sort it from biggest to smallest.
- Give a seat for each of the top 120 quotients. Whichever party a quotient belongs to wins that seat.
- Count each party's seats. That's its total entitlement. Its electorate winners are included, and list MPs make up the rest.
A simple worked example
Imagine a tiny Parliament of 10 seats and four qualifying parties. These numbers are made up to keep the maths easy.
| Party | Votes |
|---|---|
| A | 41,000 |
| B | 29,000 |
| C | 18,000 |
| D | 12,000 |
Divide each party's votes by 1, 3, 5 and 7:
| Party | ÷1 | ÷3 | ÷5 | ÷7 |
|---|---|---|---|---|
| A | 41,000 | 13,667 | 8,200 | 5,857 |
| B | 29,000 | 9,667 | 5,800 | 4,143 |
| C | 18,000 | 6,000 | 3,600 | 2,571 |
| D | 12,000 | 4,000 | 2,400 | 1,714 |
The 10 largest quotients, in bold, are: 41,000 (A), 29,000 (B), 18,000 (C), 13,667 (A), 12,000 (D), 9,667 (B), 8,200 (A), 6,000 (C), 5,857 (A) and 5,800 (B).
| Party | Share of votes | Seats | Share of seats |
|---|---|---|---|
| A | 41% | 4 | 40% |
| B | 29% | 3 | 30% |
| C | 18% | 2 | 20% |
| D | 12% | 1 | 10% |
Each party's share of seats is as close as possible to its share of the votes. That's the whole point.
The real thing: 2023
In 2023, six parties qualified: National, Labour, Green, ACT and NZ First by passing 5%, and Te Pāti Māori by winning electorates. Their party votes were run through exactly this process for 120 seats. Then:
- Each party's electorate wins were subtracted from its entitlement, and list seats filled the gap.
- Te Pāti Māori won more electorates than its entitlement, creating two overhang seats and a 122-seat Parliament. See overhang seats explained.
| Party | Party vote | Seats |
|---|---|---|
| National | 38.1% | 48 |
| Labour | 26.9% | 34 |
| Green | 11.6% | 15 |
| ACT | 8.6% | 11 |
| NZ First | 6.1% | 8 |
| Te Pāti Māori | 3.1% | 6 (4 entitled, plus 2 overhang) |
Why Sainte-Laguë?
Different formulas favour different kinds of party:
- D'Hondt (dividing by 1, 2, 3, 4...) tends to favour bigger parties slightly.
- Sainte-Laguë (dividing by 1, 3, 5, 7...) is more even-handed between big and small parties.
New Zealand's Royal Commission on the Electoral System recommended Sainte-Laguë, and it has been used at every MMP election since 1996.
What it means on election night
- The last few seats are knife-edge. The 119th and 120th quotients are often very close, so a tiny change in the vote can move one seat between parties.
- Wasted votes help everyone else. Votes for parties that don't qualify aren't included, so qualifying parties share all 120 seats.
- A projection is only as good as the count. Early numbers move as more votes come in. See why early results change.
Questions and answers
How are seats calculated in New Zealand elections?
Using the Sainte-Laguë method. Qualifying parties' party votes are divided by 1, 3, 5, 7 and so on, and the 120 largest results each win a seat.
What does Sainte-Laguë mean?
It's a method for sharing seats proportionally, named after French mathematician André Sainte-Laguë. New Zealand has used it since the first MMP election in 1996.
Why not just round each party's percentage?
Rounding percentages doesn't always add up to exactly 120. Sainte-Laguë always produces exactly the right number of seats.
Can I calculate seats myself?
Yes. Our seat builder uses the same formula. Move the party vote sliders and see the seats change.
Does the electorate vote affect the calculation?
Only in two ways: winning an electorate qualifies a party even below 5%, and winning more electorates than a party's entitlement creates overhang seats.
Sources
- Electoral Commission: seat allocation rules.
- 2023 New Zealand general election: 2023 result.
This guide is general information about New Zealand elections, checked against the sources linked above on 3 November 2026. For anything about your own enrolment or vote, check vote.nz or call the Electoral Commission on 0800 36 76 56.
Keep reading
How MMP works in New Zealand: party vote, electorate vote and 120 seats
A clear explanation of New Zealand's MMP voting system: your two votes, how seats are shared out, list MPs, the 5% threshold, overhang and why coalitions are normal.
The 5% threshold and the electorate "lifeboat" explained
Why a party on 4.9% can get no seats while one on 1% gets in. How New Zealand's 5% threshold and one-electorate rule work, with real examples from past elections.
Overhang seats explained: why Parliament can have more than 120 MPs
New Zealand's Parliament is meant to have 120 seats, but in 2023 it had 122, then 123. Here's how overhang works, every time it's happened, and why it moves the majority line.