# Depreciation Calculator

This depreciation calculator uses three different methods to estimate how fast the value of an asset decreases over time. You can use it to compare three models - the straight line depreciation, declining balance depreciation, and the sum of years digits depreciation - and decide which one suits your case best.

For a more specific model regarding automobiles, check out the car depreciation calculator!

## What is depreciation?

Imagine that you bought a cell phone at a certain price. After a few months, you decide you'd like to sell it on eBay. The problem is, you're not sure what price you should call. The value of the phone has depreciated over the last few months, so it's undoubtedly worth less now - but how much is it worth exactly?

This depreciation calculator offers you three methods to determine the value of an asset after a certain time has passed. You can find the depreciation formulas describing each of them below. They use the following symbols:

**n**is the lifetime of the asset,**OV**is the original value of the asset,**RV**is the residual value of the asset - its value after the lifetime has elapsed. It is usually assumed that it is equal to zero,**m**is the number of years that have passed between the moment when the asset was at its initial value and now.

## Straight-line depreciation

The least complicated depreciation model is the straight-line depreciation. In this model, you have to apply the following depreciation formula:

`annual expense = (OV - RV) / n`

In this model, the asset loses its value at a constant rate. Every year, the depreciation expense is exactly the same. Even though it doesn't describe the reality most accurately, it is often used due to its straightforwardness.

If you want to calculate the end book value of your asset after a certain number of years have passed, you have to use this equation:

`end book value = OV - m * [(OV - RV) / n]`

Remember that you don't have to calculate this value manually - you can plug the values into this straight line depreciation calculator and let it do the math for you!

## Declining balance depreciation

The second model describing depreciation is the declining balance depreciation. Each year, the expense is calculated as a percentage of the book value that the asset had the previous year. You can write this down with the following depreciation formula:

`annual expense = = [OV * (1 - p)^(m - 1)] * p`

where **p** is the depreciation rate, expressed as a percentage. This rate can be calculated for an asset of known lifetime and a non-zero residual value as

`p = 1 - (RV / OV)^(1 / n)`

.

Our declining balance depreciation calculator can also find out the end book value of your asset after a specific number of years have passed. It uses the following equation:

`end book value = OV * (1 - p) ^ m`

This method gives results that are much closer to reality than when using the straight line depreciation model. Still, it has its limits - the most significant issue of this method being its complexity.

## Sum of years digits depreciation

The last method is an accelerated depreciation model that assumes that depreciation slows down with each passing year. Instead of a fixed depreciation rate, it assigns a fraction of total depreciation costs to each year of the asset's lifetime.

In order to use this model, you need to calculate the depreciation base according to the formula

`d = (OV - RV)`

Then, you have to divide it by the sum of years digits:

`D = d / (1 + 2 + 3 + ... + n)`

The number `(1 + 2 + 3 + ... + n)`

is a sum of a finite arithmetic sequence, and can hence be calculated as

`1 + 2 + 3 + ... + n = (n + 1) * n / 2`

After calculating the value of **D**, you can use the following depreciation formula to find the annual expense:

`annual expense = D * (n - m + 1)`

It means that if the lifetime of your asset is equal to 5 years, then during the first year, the expense will be equal to 5/15 of the depreciation base. During the second year, it will be equal to 4/15 of the base, during the third - to 3/15, etc. All of these fractions should add up to 1.

Our sum of years digits calculator can also find the end book value with the following equation:

`end book value = OV - D * [m * n - (m - 1) * m /2]`

If you're using this method, your initial depreciation expenses will be substantially higher than the ones in following years. Also, keep in mind that most tax systems don't allow for using this model.