# How many grains are in a teaspoon of sugar?

Mathematician James Grime quizzed the rest of The Naked Scientists Q&A show panel...
05 September 2017

## Question

How many grains in a teaspoon of sugar?

The team guess how many grains in a teaspoon of sugar...

Beverley - I can think of how to do it. I can't think what the number would end up like.

James - Just talk us through what you would think.

Beverley - Well, I need to know the volume of my grain of sugar. Was it granulated or castor? I think we agreed castor. I need to know the volume of my teaspoon and then that’s a fairly simple sum. The volume of teaspoon is presumably quite hard. Oh no, we know what it is. It’s 5 ml. It would be quite hard to calculate.

James - I think your method is excellent.

Chris - You have to give us a number. You can't get out of it so what's your number?

Beverley - 50 million.

Chris - Okay, 50 million from Beverley. Jess?

Jess - I weigh lots of small stuff in the lab. I work in printed electronics with these tiny, tiny little amounts of polymers or small molecule. I would say that a grain of sugar weighs about half a milligram?

James - Yeah. It’s about – I've got here 0.2 milligrams.

Jess - Okay, so I'm going to go with like 25,000.

Chris - So how many do you have? 25,000 particles. And Peter?

Peter - I'm going to use a special number, 3 to the power of 6.

James - 3 to the power of 6.

Peter - 729. Now I know it’s too low but I suspect…

Chris - Not 42?

Peter - No, I couldn’t get it that low.

Chris - So James, you better tell us then to put us out of our misery then. Who’s closest?

James - Well, I think a very excellent answer was Jess with her 25,000. I have an answer here of 20,000 based on 4 grams of sugar weighing about 0.2 milligrams.

Chris - Okay, so can you show us your working because that’s very important in maths to show your working, isn’t it? So how did you do that and you have to do it in 30 seconds.

James - So, like Beverley’s method, we can look at how big the crystals are. The diameter of a crystal might be about 0.7 millimetres. We have to look at how efficiently they're packed in as well, because there is space in-between them. So we’re thinking about 60 per cent packed in and, going through the calculations, we will get the answer 20,000.