The Criss-Cross Method for Ionic Formulas

The criss-cross method (also called “swap and drop”) is a quick shortcut for writing the formula of an ionic compound once you know the charges on its ions. You swap the charge numbers so each becomes the subscript of the other ion, then simplify. It’s fast and reliable — as long as you understand why it works and remember one crucial final step. This guide explains the method, the reasoning behind it, and the traps to avoid.

Why ionic formulas need balancing

An ionic compound is made of positive and negative ions, and the compound as a whole has no overall charge (see ionic bonding explained). So the total positive charge from the cations must exactly equal the total negative charge from the anions. The formula shows the smallest whole-number ratio of ions that achieves this.

The criss-cross method is simply a fast way to find that ratio.

The method in four steps

1. Write the symbols of both ions with their charges, cation first.
2. Swap the numbers of the charges (ignore the + and − signs): the cation’s charge number becomes the anion’s subscript, and the anion’s charge number becomes the cation’s subscript.
3. Simplify to the lowest whole-number ratio if both subscripts share a common factor.
4. Drop subscripts of 1, and put brackets around polyatomic ions that have a subscript greater than 1.

Worked examples

Example 1: aluminium oxide

1. Al³⁺ and O²⁻
2. Swap: Al gets 2, O gets 3 → Al₂O₃
3. 2 and 3 share no common factor.
4. Al₂O₃

Check: 2 × (+3) = +6; 3 × (−2) = −6. ✓

Example 2: calcium chloride

1. Ca²⁺ and Cl⁻
2. Swap: Ca gets 1, Cl gets 2 → Ca₁Cl₂
3. No simplification needed.
4. Drop the 1 → CaCl₂

Example 3: magnesium nitride

1. Mg²⁺ and N³⁻
2. Swap → Mg₃N₂
3. No common factor.
4. Mg₃N₂

Check: 3 × (+2) = +6; 2 × (−3) = −6. ✓

Example 4: the simplification step — magnesium oxide

1. Mg²⁺ and O²⁻
2. Swap → Mg₂O₂
3. Simplify 2 : 2 to 1 : 1 → MgO
4. MgO

This is the step people most often forget. “Mg₂O₂” is wrong — ionic formulas always use the lowest ratio.

Example 5: lead(IV) oxide

1. Pb⁴⁺ and O²⁻
2. Swap → Pb₂O₄
3. Simplify 2 : 4 to 1 : 2 → PbO₂
4. PbO₂

Example 6: a polyatomic ion — calcium hydroxide

1. Ca²⁺ and OH⁻
2. Swap → Ca₁(OH)₂
3. No simplification.
4. Ca(OH)₂

The hydroxide ion must be in brackets, because the subscript 2 applies to the whole OH group. Without brackets, “CaOH₂” would mean one oxygen and two hydrogens.

Example 7: aluminium sulfate

1. Al³⁺ and SO₄²⁻
2. Swap → Al₂(SO₄)₃
3. No common factor.
4. Al₂(SO₄)₃

Never change the numbers inside a polyatomic ion. The 4 in SO₄ is part of the ion’s identity; only the number outside the bracket changes.

Example 8: ammonium phosphate

1. NH₄⁺ and PO₄³⁻
2. Swap → (NH₄)₃(PO₄)₁
3. No simplification.
4. (NH₄)₃PO₄

Example 9: iron(III) sulfate

1. Fe³⁺ (from the Roman numeral — see naming compounds with transition metals) and SO₄²⁻
2. Swap → Fe₂(SO₄)₃
3. Fe₂(SO₄)₃

Example 10: when the charges are equal — sodium chloride, calcium carbonate

• Na⁺ and Cl⁻ → Na₁Cl₁ → NaCl
• Ca²⁺ and CO₃²⁻ → Ca₂(CO₃)₂ → simplify → CaCO₃

Why the method works

Swapping the charge numbers is a shortcut for finding the lowest common multiple (LCM) of the two charges.

Take Al³⁺ and O²⁻. The LCM of 3 and 2 is 6. To reach +6 you need 2 Al³⁺; to reach −6 you need 3 O²⁻. Criss-crossing gives exactly those numbers, because each ion’s subscript equals the other ion’s charge, so:

(cation charge × anion charge) = (anion charge × cation charge)

— the totals always balance. When both charges share a factor (like 2 and 2, or 4 and 2), the swap gives a multiple of the true ratio, which is why you must simplify.

Working backwards: charge from formula

The method can also be reversed to find an unknown charge — useful for naming transition metal compounds.

Example: What’s the charge on iron in Fe₂O₃?

• Oxide is O²⁻; three of them give −6.
• Two iron atoms must give +6 → each is +3 → iron(III) oxide.

Be careful: you can’t simply “un-cross” the subscripts, because the formula may have been simplified. In FeO, un-crossing would suggest Fe⁺ and O⁺ — nonsense. Always calculate from the known anion charge instead.

When not to use it

• Covalent compounds — such as CO₂, N₂O₄ and SF₆ — don’t contain ions, and their formulas come from the prefixes in the name, not from charges (see how to write chemical formulas from names).
• Ions that are already paired, such as the mercury(I) ion, Hg₂²⁺. Mercury(I) chloride is Hg₂Cl₂, and simplifying it to HgCl would be wrong because Hg₂²⁺ is a single ion. Similarly, the peroxide ion O₂²⁻ stays as O₂²⁻: sodium peroxide is Na₂O₂, not NaO.

Why understanding beats the shortcut

The criss-cross method is fast, but it’s worth knowing the charge-balancing reasoning behind it, because the reasoning never fails while the shortcut sometimes does. If you balance charges directly — asking “how many of each ion do I need so the totals cancel?” — you’ll automatically get the lowest ratio, you won’t be tempted to simplify paired ions like Hg₂²⁺, and you’ll be able to work backwards from a formula to an unknown charge.

A good habit is to use criss-cross to get a quick answer, then check it by multiplying each subscript by its ion’s charge and confirming the total is zero. That check takes seconds and catches nearly every mistake, including the most common one: forgetting to simplify, as in Mg₂O₂ or Ca₂(CO₃)₂. Over time, the balancing becomes so automatic that you barely need the shortcut at all.

Common mistakes

• Forgetting to simplify: Mg₂O₂ → MgO.
• Simplifying when you shouldn’t: Hg₂Cl₂ and Na₂O₂ contain paired ions.
• Missing brackets around polyatomic ions: Mg(NO₃)₂, not MgNO₃₂.
• Changing subscripts inside polyatomic ions.
• Carrying the signs into the subscripts: subscripts are always positive numbers.
• Using the method for covalent compounds.

Practice

Use criss-cross to write formulas for:

1. potassium oxide (K⁺, O²⁻)
2. barium phosphate (Ba²⁺, PO₄³⁻)
3. tin(IV) sulfide (Sn⁴⁺, S²⁻)
4. copper(II) nitrate (Cu²⁺, NO₃⁻)
5. calcium sulfate (Ca²⁺, SO₄²⁻)
6. chromium(III) oxide (Cr³⁺, O²⁻)

Answers:

1. K₂O
2. Ba₃(PO₄)₂
3. Sn₂S₄ → simplify → SnS₂
4. Cu(NO₃)₂
5. Ca₂(SO₄)₂ → simplify → CaSO₄
6. Cr₂O₃

Key takeaways

• Swap the charge numbers to become subscripts, then simplify to the lowest ratio.
• Drop subscripts of 1; bracket polyatomic ions with subscripts above 1.
• The method works because it finds the lowest common multiple of the charges.
• Don’t use it for covalent compounds or for paired ions like Hg₂²⁺ and O₂²⁻.
• Always check that total positive and negative charges balance.

For the ion charges you’ll need, see common ions and their charges.