BC to AD math, minus the off-by-one.

7:40 pm · the kitchen table

The homework question that trips everyone up

The worksheet says the Rosetta Stone decree was carved in 196 BC and that Jean-François Champollion announced he could read it in 1822. Question 4: how many years apart? Your child writes 2,018. You check it, nod, and you are both wrong by one.

Adding the two numbers feels right, and it nearly is. The catch is that the calendar jumps straight from 1 BC to AD 1. There is no year zero to cross, so simple addition counts one year that never existed. The real answer is 2,017. That is what the calculator above shows on its first load.

Crossing from BC into AD? Add the two years, then take away one.

The rule

How do you calculate years between BC and AD?

Add the BC year to the AD year, then subtract 1, because the calendar has no year 0. From 196 BC to AD 1822 is 196 + 1822 − 1 = 2,017 years. If both dates are BC, or both are AD, just subtract the smaller number from the larger one. No adjustment is needed.

Astronomers sidestep the problem by writing years as plain numbers with a year 0. NASA's eclipse site explains that in this "astronomical" numbering, year 0 is 1 BCE and −1 is 2 BCE, so any BCE year x becomes −(x − 1). Our calculator does exactly that behind the scenes, then subtracts.

The calculator converts BC to astronomical years first, so the off-by-one cannot sneak in.

Before you download anything

Who should use something else

If you only need the arithmetic, the calculator on this page is the whole job, and you are welcome to bookmark it. PastRush is a game about evidence, not a date converter.

• Kids under 9: PastRush is rated 9+ on the App Store, and its cases ask for real reading.
• Fast trivia fans: if you want quick-fire "which came first" rounds and nothing else, a card game like Timeline or a daily trivia app will feel lighter.
• Exact day counts: neither this calculator nor the app counts days or months. Both work in whole calendar years.

Need only the number? This page is enough. Need the habit of checking evidence? That is what the app is for.

Inside the app

Chronology practice for kids, with real case files

PastRush turns date order into a detective job. In its Chronology challenges you rebuild the order of events, and the listing says BC/AD dates are "handled correctly". Six investigations are free for everyone: the Rosetta Stone, Pompeii, the rock layers of the Grand Canyon, Ötzi the Iceman, continental drift and the Norse in Vinland.

A true-scale time bar shows how far apart two events really are, which is the same idea as the gold bar under our calculator. Every answer explains why and links to the source behind it.

Six of the twelve cases are free, with no account and no ads.

Worked examples

BC to AD timeline examples you can check

Here are three gaps from cases in the app, each with a published date. Tap the matching chip under the calculator and the numbers should agree.

1. Rosetta decree to discovery: 1,994 years, not 1,995. Live Science's history column dates the decree to 196 BC and the stone's discovery to 1799. So 196 + 1799 − 1 = 1,994 years.
2. Decree to decipherment: 2,017 years. The same article dates Champollion's announcement to 27 September 1822.
3. Norse wood-cutting to today: 1,005 years. A 2021 study in Nature, summarised by the University of Groningen, used a solar-storm signal in tree rings to date woodworking at L'Anse aux Meadows to AD 1021. Both dates are AD, so 2026 − 1021 = 1,005.

Honest limit: many ancient dates are approximate. A gap between two "about" dates is only as exact as the dates themselves, so write "about 2,000 years" when your source says "about".

A precise answer from fuzzy dates is still fuzzy. Say "about" when the source does.

Three ways to count

How many years from 1 BC to AD 1?

One. That tiny case is the best test of any method, so here is how the common approaches score on it and on our Rosetta example.

We built the calculator on the third method because it never needs a special case, even for two BC dates. The design choice in PastRush is similar: in its Which Came First? rounds, dates that historians still debate are left out, so every round has one right answer.

Test any method with 1 BC to AD 1. If it says 2, it is counting a year that never happened.

Quick answers

BC and AD questions parents ask