# Depreciation Calculator

Created by Bogna Szyk and Tomasz Jedynak, PhD
Reviewed by Jack Bowater
Based on research by
Cipra T. Financial and Insurance Formulas (2006)
Last updated: Oct 10, 2022

The 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, the declining balance depreciation, and the sum of years digits depreciation — to decide which one suits you best. Read on to find answers for the following questions:

• What is depreciation and what does depreciate mean?
• What are the most common methods of depreciation?
• What is the residual value?
• How to calculate depreciation? Especially, how to calculate straight line depreciation? How to calculate the declining balance depreciation and how to calculate the sum of years digits depreciation?

From this article, you will know how to calculate depreciation expense and how to calculate accumulated depreciation.

## What is depreciation? — the depreciation definition

Imagine that you bought a personal computer for a certain price. After a few months, you decide you'd like to sell it. The problem is, you're not sure how much it's worth now. The present value of the computer is certainly lower than the amount you bought it for a few months ago. An economist would say here that your computer has depreciated over the last few months. So we can say that the fundamental concept of depreciation is to reflect the reduction in value of an asset over time, due to factors such as wear and tear and the appearance of new and better products on the market.

The more formal definition of depreciation says that it is the method of calculating the cost of an asset over its lifespan. In accounting, depreciation is perceived as a method of reallocating the cost of a tangible asset over its useful lifespan. To fully understand this approach, let's study the following situation.

When a company purchases a highly valuable tangible asset (e.g., machinery or vehicle), such a large expense can have a substantial impact on the yearly income statement of the company. So, to omit the sharp changes in the income statement, the purchase of expensive assets is smoothed in the accounting books by presenting the asset as an expense over its useful lifetime. It means that each year, only a part of the value of an asset is posted as current expenses. Such an approach allows the company to evenly spread the costs over the whole period of use.

## Methods of depreciation

In practice, several different methods for calculating depreciation are used. These methods can be either based on the passage of time or the degree of usage the asset undergoes. The following depreciation methods can be applied to different types of tangible assets:

• Straight-line depreciation;
• Declining balance method;
• Double declining balance method;
• Annuity depreciation;
• Sum-of-years-digits method;
• Units-of-production depreciation method;
• Units of time depreciation;
• Group depreciation method; and
• Composite depreciation method.

Note that at the end of an asset lifespan, the total amount of its depreciation will be identical, no matter which method of depreciation is applied. The only thing that varies over the different methods of depreciation is the timing (the amount of money that is depreciated over the smaller periods).

In the further part of this text, we will focus on the description of the three most commonly used types of depreciation: the straight line depreciation, the declining balance depreciation, and the sum of years digits depreciation. We're going to pay attention especially to the depreciation formulas and the detailed explanation of how to calculate the value of depreciation with each of them.

## Residual value and depreciation

As was already mentioned, residual value (salvage value) is an estimated amount of money that an asset will be worth after the planned number of years of use. Obviously, in real life, it is impossible to accurately predict the exact salvage value of an asset after a particular number of years.

That means that the salvage value is only an approximation. However, in accounting, this approximation is just a kind of a transition state — because when you sell an asset, if the cash received for it is greater than its net book value (initial value minus accumulated depreciation), you will need to record a gain on sale. On the other hand, if you sell an asset below its net book value, you will need to record a loss on sale.

Note here that, if this number of years in use is equal to the product lifetime, the residual value is zero.

## Car depreciation calculator

For sure, one of the most interesting cases of depreciation is the loss of value of a motor vehicle. As you probably know, the value of a brand new car decreases sharply as soon as you drive off of the car dealership — experts say that the value of a car decreases to 91% of the initial value the minute you purchase it! Over the next years, the value of the car decreases, until after several years (around 10 to 11), it reaches zero value. Obviously, you will still be able to sell it. However, its market value will be very low. To avoid the hassles of selling a used car, many people prefer leasing a car these days instead of buying one.

If you are interested in detailed car depreciation calculations, be sure to look at our car depreciation calculator. It uses a model more specific to automobiles.

## How to use our depreciation calculator?

Our smart depreciation calculator lets you compute the yearly depreciation and to determine the value of an asset after a certain amount time has passed. The yearly depreciation is calculated on the basis of the three most commonly used methods: straight line depreciation, the declining balance depreciation, and the sum of years digits depreciation.

To get results using our calculator, all you need to do is to fill in four fields:

• Original cost — the original value of the asset (purchasing price).
• Residual value — an estimated amount of money that an asset will be worth after the lifetime has elapsed (it is usually assumed that it is equal to zero, for more information see section ).
• Lifetime — the estimated number of years the asset is likely to remain in service.
• End book value after… — in this field, you should provide the year after which you would like to compute the book value of the asset.

And that's it! In a moment, our depreciation calculator computes three variants of depreciation. If you are curious how it works, you should get familiar with the depreciation of the formulas described in the following sections of the article. Each formula uses the same set of symbols:

• $\text{OV}$ is the original cost (value) of the asset,
• $\text{RV}$ is the residual value of the asset,
• $n$ is the lifetime of the asset,
• $m$ is the number of years that passed between when the asset was purchased and the date you want to sell it, so it corresponds with the field End book value after… in the calculator.

## Straight-line depreciation

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

$\small \text{annual expense} = \frac{\text{OV} -\text{RV}}{n}$

In this model, the asset loses its value at a constant rate. Every year, the depreciation expense is exactly the same. Even though this isn't the most accurate description of depreciation, 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:

$\small \text{end book value} \\ = \text{OV} - m \times \frac{\text{OV} - \text{RV}}{n}$

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 as

$\small \text{annual expense} \\ = p\times\text{OV} \times (1 - p)^{m - 1}$

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

$\small p = 1 - (\text{RV} / \text{OV})^{1/n}$

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:

$\small \text{end book value} = \text{OV} \times (1 - p) ^ m$

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.

$\small d = (\text{OV} - \text{RV})$

Then, you have to divide it by the sum of the amount of years prior to its residual value reaching zero:

$\small D = d / (1 + 2 + 3 + ... + n)$

The number $(1 + 2 + 3 + ... + n)$ is a sum of a finite arithmetic sequence, and can hence be calculated as

$\small 1 + 2 + 3 + ... + n \\ = (n + 1) \times \frac{n}{2}$

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

$\small \text{annual expense} \\ = D \times (n - m + 1)$

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 $\frac{5}{15}$ of the depreciation base. During the second year, it will be equal to $\frac{4}{15}$ of the base, during the third to $\frac{3}{15}$, etc. All of these fractions should add up to $1$.

Our sum of years digits calculator can also be used to find the end book value:

$\small \text{end book value} \\ = \text{OV} - Dmn - \frac{D m \times (m - 1)}{2}$

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

Bogna Szyk and Tomasz Jedynak, PhD
Original cost
$Residual value$
yrs
End book value after...
yrs
Straight line depreciation
Depreciation expense
$End book value$
Declining balance depreciation
Depreciation rate
%
Depreciation expense
$End book value$
Sum-of-years' digits depreciation
Depreciation expense
$End book value$
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