# The dip to litres formula

> Derives and works the formula for the litres in a horizontal flat-ended cylindrical fuel tank at a given dip, from the circular segment area, with a full numerical example and IOCL deadwood.

Canonical: https://dipdensity.watsinfo.com/guides/dip-to-litres-formula/
Last updated: 2026-11-02

**Short answer:** Litres = L × [r² · acos((r − h) / r) − (r − h) · √(2rh − h²)] ÷ 1000, with r the inside radius, h the dip and L the length, all in cm. For a tank 210 cm across and 600 cm long at a dip of 142.5 cm, that is 15,013.36 litres.

## The shape

An underground fuel tank lies on its side: a cylinder with flat ends. Looking at one end, the fuel fills the bottom of a circle up to the dip. That shape is a **circular segment**. The litres are the segment's area times the tank's length.

## The formula

With **r** the inside radius, **h** the dip and **L** the length, all in centimetres:

```
segment area = r² · acos((r − h) / r) − (r − h) · √(2rh − h²)     (cm²)
litres       = segment area × L ÷ 1000
```

The first part, r² · acos(...), is the slice of the circle the segment sits in. The second part takes off the triangle between the slice's edges and the centre.

## Worked example: BPCL 20 KL, 210 cm across

r = 105 cm, L = 600 cm, h = 142.5 cm.

1. r − h = 105 − 142.5 = −37.5
2. (r − h) / r = −0.357143; acos(−0.357143) = 1.936004 radians
3. r² · acos = 11,025 × 1.936004 = 21,344.44
4. 2rh − h² = 29,925 − 20,306.25 = 9,618.75; √ = 98.0752
5. (r − h) · √ = −37.5 × 98.0752 = −3,677.82
6. area = 21,344.44 − (−3,677.82) = 25,022.26 cm²
7. litres = 25,022.26 × 600 ÷ 1000 = **15,013.36 L**

This is the figure the app shows for the same tank and dip. The [calculator](https://dipdensity.watsinfo.com/tools/tank-volume-calculator/) does it for any tank.

## Deadwood

IndianOil prints a deadwood figure on its charts: litres taken up by fittings inside the tank. Take it off in proportion:

```
litres = cylinder litres × (1 − deadwood ÷ full cylinder litres)
```

For the IOCL 20 KL tank the deadwood is 18 litres.

## Questions

### Does acos work in degrees or radians?

Radians. In a spreadsheet, ACOS already returns radians, so =L*(r^2*ACOS((r-h)/r)-(r-h)*SQRT(2*r*h-h^2))/1000 works as it is.

### Why not just use the full litres times the dip over the diameter?

Because a tank is round. Near the bottom and the top each centimetre holds little; in the middle each centimetre holds most. A straight line is wrong by hundreds of litres in a 20 KL tank.