Choose a mode and enter your numbers. In download time mode, a graph also shows how the time depends on the speed.
Prefixes are decimal (1 KB = 1,000 B, 1 MB = 1,000,000 B), and 1 byte = 8 bits. Fields you do not use can be left blank.
Result and graph
Choose a mode on the left, enter your numbers and press "Calculate". The time, converted values and a graph will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter a file size and an internet speed, and you see how long the download or upload takes on the spot (in seconds and also in an easy-to-read form such as "22 min 13 s")
- Converts between bits, bytes (B), KB, MB, GB, TB, Kbit, Mbit, Gbit and Tbit, all in one table
- Also estimates the bandwidth a website needs (page views, average page size and a redundancy factor) and the average bandwidth of web hosting (monthly data ÷ days)
- In download time mode, a graph shows how the time shrinks as the speed goes up (an inverse relationship)
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The prefixes on this page (K, M, G, T) are decimal (powers of 1,000), as is usual for networking. 1 KB = 1,000 B, 1 MB = 1,000,000 B, and 1 byte = 8 bits. Computers sometimes show file sizes in binary units (powers of 1,024, written KiB, MiB, GiB), so the same "1 GB" can differ depending on the base (see the Terms section below). The results are theoretical estimates; real transfers are a little slower because of protocol overhead and network congestion.
What is this calculation used for?
Knowing ahead how long a big download will take
"How long will a 50 GB game take on a 300 Mbps connection?" 50 GB is \(50 \times 8 = 400\) gigabits, and \(400{,}000 \div 300 \approx 1{,}333\) seconds, or about 22 minutes 13 seconds.
Knowing the wait lets you plan, such as starting the download before bed or skipping it right before you leave. You can also see the inverse relationship: double the speed and the time is cut in half.
Checking whether your internet plan is fast enough for streaming and video calls
Streaming video and video calls need a steady minimum speed to play without stopping. If you assume about 5 Mbps per HD stream, three people watching in different rooms at the same time need about \(5 \times 3 = 15\) Mbps.
When you move or change plans, knowing in numbers the speed your household actually needs makes choosing a plan easier.
Estimating server bandwidth for a website or app (infrastructure work)
Before launching a site, you estimate the bandwidth needed to handle the traffic. If pages are viewed 10 times per second and each page is 2 MB, you need \(10 \times 2\,\text{MB} \times 8 = 160\) Mbps (with a redundancy factor of 1).
Adding headroom with a redundancy factor for traffic spikes is standard practice, and the result is the basis for choosing a server or cloud plan.
Keeping track of your phone's data allowance
With a plan that includes 20 GB of high-speed data a month, watching 200 MB videos uses it up after about \(20{,}000 \div 200 = 100\) videos (in decimal, 20 GB = 20,000 MB).
Knowing how many videos' worth you have left helps you avoid being slowed down at the end of the month and decide when to switch to Wi-Fi.
Planning cloud backups and large transfers
Uploading 1 TB of data to the cloud on a 1 Gbps connection takes \(8 \times 10^{12} \div 10^{9} = 8000\) seconds (about 2 hours 13 minutes).
Estimating the transfer time up front lets you plan, such as running it overnight outside business hours or upgrading the connection. It is an essential calculation for data migrations and server moves.
Formulas and figures
Download time (data ÷ speed)
Figure
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(t\)
\(=\)
\(S\)
\(\div\)
\(v\)
③
time \(t\)
\(=\)
①
data \(S\)
\(\div\)
②
speed \(v\)
The formula in words
①
Divide
the data size \(S\) (bits)
by
②
the speed \(v\) (bits that can be sent per second)
,
③
and you get the
time \(t\) (seconds)
Quick example
Downloading a 100 MB file (= 800 megabits) on a 10 Mbps connection takes
time
\(=\)
800 megabits (data)
\(\div\)
10 Mbps (speed)
\(100 \times 8 = 800\)
\(800 \div 10 = 80\)
Key idea
The trick is to put both the data size and the speed in bits. File sizes are usually given in bytes (B, KB, MB…) and internet speeds in bits per second (bps), so the units do not match. First multiply the data size by 8 to turn it into bits (1 byte = 8 bits). If both use the same prefix "M" (mega), as in 800 megabits ÷ 10 megabits per second, the prefixes cancel and you can divide directly. Here the answer is 80 seconds.
Converting bytes to bits (\(1\) byte \(=8\) bits)
Figure
Standard notation
(the usual math form)
In words
(symbols replaced with words)
\(b\)
\(=\)
\(B\)
\(\times\)
\(8\)
③
bits \(b\)
\(=\)
①
bytes \(B\)
\(\times\)
②
8 (constant)
The formula in words
①
Multiply
the number of bytes \(B\)
by
②
8 (bits per byte)
,
③
and you get the
number of bits \(b\)
Quick example
Converting 1,000 bytes (B) to bits gives
bits
\(=\)
1000 (bytes)
\(\times\)
8
\(1000 \times 8 = 8000\)
Key idea
A bit is one piece of information, a 0 or a 1, and a byte is a group of 8 bits, so 1 byte = 8 bits. File sizes are traditionally given in bytes and connection speeds in bits, so always put them in the same unit before calculating a time. Large numbers are shortened with prefixes (K, M, G, T). This page uses the decimal prefixes that are standard in networking (1 K = 1,000, 1 M = 1,000,000, 1 G = 1,000,000,000). Note that the binary units some computers use for storage (powers of 1,024, written KiB, MiB, GiB) are based on a different number.
Website bandwidth (page views × page size × redundancy factor)
Figure
Standard notation
(the usual math form)
\(W\)
\(=\)
\(r\)
\(\times\)
\(P\)
\(\times\)
\(f\)
In words
(symbols replaced with words)
④
bandwidth needed \(W\)
\(=\)
①
views per second \(r\)
\(\times\)
②
page size \(P\)
\(\times\)
③
redundancy \(f\)
The formula in words
①
Multiply
the page views per second \(r\)
by
②
the page size \(P\) (bits)
and by
③
the redundancy factor \(f\) (headroom for busy times)
,
④
and you get the
bandwidth needed \(W\) (bits per second)
Quick example
For a site with 10,000 page views a day, an average page size of 2 MB (= 16,000,000 bits) and a redundancy factor of 1.5
bandwidth needed
\(=\)
views per second (≈ 0.1157)
\(\times\)
16,000,000 bits
\(\times\)
1.5
\(\dfrac{10000}{86400} \approx 0.1157\)
\(\dfrac{10000}{86400} \times 16000000 \times 1.5 \approx 2777778\)
Key idea
First turn the page views into views per second (for a day, divide by 86,400 seconds). Multiply that by the data per view (in bits), and you get the average number of bits sent per second, which is the bandwidth needed. Here it is about 2,777,778 bits per second, or about 2.78 Mbps. If you plan only for the average, though, you will run short at moments when traffic spikes, so multiply by a redundancy factor (such as 1.5 to 2) to leave headroom.
Hosting bandwidth (monthly data ÷ seconds in the period)
Figure
Standard notation
(the usual math form)
\(W\)
\(=\)
\(Q\)
\(\div\)
\(d \times 86400\)
In words
(symbols replaced with words)
③
average bandwidth \(W\)
\(=\)
①
monthly data \(Q\)
\(\div\)
②
seconds (days \(d\) × 86400)
The formula in words
①
Divide
the monthly data \(Q\) (bits)
by
②
the seconds in the period (days \(d\) × 86,400 seconds per day)
,
③
and you get the
average bandwidth \(W\) (bits per second)
Quick example
The average bandwidth of a server that sends out 1 TB (= 8 trillion bits) in a month (30 days) is
average bandwidth
\(=\)
8,000,000,000,000 bits
\(\div\)
2,592,000 s (30 days)
\(30 \times 86400 = 2592000\)
\(\dfrac{8000000000000}{2592000} \approx 3086420\)
Key idea
Divide the total data sent in a month by the number of seconds in the period (days × 86,400), and you get the average number of bits sent per second, the average bandwidth (here about 3.09 Mbps). This is a smoothed-out average, so at busy times of day you need a higher speed than this. The same formula also works the other way, to estimate how much data you can send in a month with the bandwidth in your plan.
The core formula is "time = data ÷ speed", and you always convert to bits first (1 byte = 8 bits, with decimal prefixes based on 1,000). Extending the same idea, the bandwidth a website needs is "page views per second × page size × redundancy factor", and the average hosting bandwidth is "monthly data ÷ seconds in the period". The key point is that doubling the speed cuts the time in half (an inverse relationship).
Symbols and terms
Symbols
| \(t\) | tee | The time (seconds). It is the data size divided by the speed. (From "time".) |
| \(S\) | S | The data size (bits), the size of the file to download expressed in bits. (From "size".) |
| \(v\) | vee | The speed (the number of bits that can be sent per second). (From "velocity".) |
| \(W\) | W | The bandwidth (bits per second), the most data that can be sent per second. On this page it stands for the bandwidth needed or the average bandwidth. (From "width" in "bandwidth".) |
| \(f\) | f | The redundancy factor, how many times the needed bandwidth to plan for, to handle busy times (1 for no extra room). (From "factor".) |
Terms
| bit | The smallest unit of information, a single 0 or 1. Data sizes and connection speeds are, at bottom, counts of bits. |
| byte | A unit made of 8 bits (1 byte = 8 bits). File sizes are usually given in bytes (B, KB, MB…). |
| bandwidth | The most data that can be sent per second. It is often compared to the number of lanes on a highway - the wider it is, the more data can flow at once. It is measured in bits per second (bps). |
| throughput | The speed at which data is actually being transferred. If bandwidth is the width of the highway (the theoretical maximum), throughput is the amount of traffic actually moving, which is lower than the bandwidth because of congestion and protocol overhead. |
| bps (bits per second) | The unit of connection speed, the number of bits sent per second. Mbps is a million bits per second and Gbps is a billion bits per second. Internet speeds are usually given in this unit. |
| decimal prefix | Prefixes K, M, G and T that each go up by a factor of 1,000 (1 KB = 1,000 B). They are the standard for connection speeds and on this page. For the same "1 GB", the value differs by about 7% from the binary prefixes, which go up by 1,024. |
| binary prefix | Prefixes that go up by a factor of 1,024, written Ki, Mi and Gi when they need to be told apart (1 KiB = 1,024 B). Some computers show storage in these units, and because the base is different, the values differ by about 7% from decimal prefixes. |
| redundancy factor | When estimating server bandwidth, the multiple of the average to provide for moments when traffic spikes. About 1.5 to 2 is common, and 1 is no extra room. |
| inverse relationship | A relationship where, when one amount becomes 2 or 3 times as large, the other becomes \(\dfrac{1}{2}\) or \(\dfrac{1}{3}\) as large (also called inverse variation). The time is inversely proportional to the speed, so the faster the speed, the shorter the time. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Division (Grades 3–4) |
|
| How units work (elementary to middle school) |
|
| Direct and inverse variation (Grades 7–8) |
|
| Large numbers and exponents (Grades 6–8) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table for the download time
| Data size (MB) | 100 |
| Speed (Mbps) | 10 |
| Time (seconds) | =B1*8/B2 |
Table to convert bytes to bits
| Data size (bytes, B) | 1000 |
| Data size (bits) | =B1*8 |
Table for the bandwidth a website needs
| Page views per day | 10000 |
| Average page size (MB) | 2 |
| Redundancy factor | 1.5 |
| Bandwidth needed (Mbps) | =B1/86400*B2*8*B3 |
Table for the average hosting bandwidth
| Monthly data (TB) | 1 |
| Days | 30 |
| Average bandwidth (Mbps) | =B1*8*1000000/(B2*86400) |
In the first table, enter the data size (MB) in B1 and the speed (Mbps) in B2, and B3 shows the time (seconds). "=B1*8/B2" says "multiply the data size by 8 to get bits, then divide by the speed". MB and Mbit use the same prefix, so it cancels out; 100 MB at 10 Mbps takes 80 seconds.
The second table just multiplies bytes by 8 to get bits (1,000 B → 8,000 bits).
The third table divides the page views by 86,400 (seconds in a day) to get views per second, then multiplies by the page size (in bits) and the redundancy factor. The example gives about 2.78 Mbps.
The fourth table converts the monthly data to bits and divides by days × 86,400 (seconds). 1 TB over 30 days is about 3.09 Mbps.
The second table just multiplies bytes by 8 to get bits (1,000 B → 8,000 bits).
The third table divides the page views by 86,400 (seconds in a day) to get views per second, then multiplies by the page size (in bits) and the redundancy factor. The example gives about 2.78 Mbps.
The fourth table converts the monthly data to bits and divides by days × 86,400 (seconds). 1 TB over 30 days is about 3.09 Mbps.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table for the download time
| Data size (MB) | 100 |
| Speed (Mbps) | 10 |
| Time (seconds) | =B1*8/B2 |
Table to convert bytes to bits
| Data size (bytes, B) | 1000 |
| Data size (bits) | =B1*8 |
Table for the bandwidth a website needs
| Page views per day | 10000 |
| Average page size (MB) | 2 |
| Redundancy factor | 1.5 |
| Bandwidth needed (Mbps) | =B1/86400*B2*8*B3 |
Table for the average hosting bandwidth
| Monthly data (TB) | 1 |
| Days | 30 |
| Average bandwidth (Mbps) | =B1*8*1000000/(B2*86400) |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the numbers in column B with your own. The prefixes are decimal (based on 1,000).
How to calculate it in Python
file_size = 100 # file size
file_unit = "MB" # unit (B/KB/MB/GB/TB)
speed = 10 # connection speed
speed_unit = "Mbit/s" # unit (bit/s, Kbit/s, Mbit/s, Gbit/s)
# decimal prefixes (based on 1000). 1 byte = 8 bits
bits_per = {"B": 8, "KB": 8_000, "MB": 8_000_000, "GB": 8_000_000_000, "TB": 8_000_000_000_000}
bps_per = {"bit/s": 1, "Kbit/s": 1_000, "Mbit/s": 1_000_000, "Gbit/s": 1_000_000_000}
file_bits = file_size * bits_per[file_unit] # data size (bits)
speed_bps = speed * bps_per[speed_unit] # speed (bits per second)
time_sec = file_bits / speed_bps # time (seconds)
print(f"Data size: {file_bits:,} bits")
print(f"Speed: {speed_bps:,} bits/s")
print(f"Time: {time_sec} s")
Runs with the standard library only. It keeps the number of bits for each unit in a dictionary, converts the data size to bits and the speed to bits per second, then divides. The example shows a time of 80 seconds. Change the four values at the top and run it.
How to write it in LaTeX and other math languages (copy and paste)
Download time (data ÷ speed)
t = S ÷ v
t = \dfrac{S}{v}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>t</mi>
<mo>=</mo>
<mfrac><mi>S</mi><mi>v</mi></mfrac>
</mrow>
</math>
t = S / v
S / v
t := S / v;
t = S / v;
t = S/v
Converting bytes to bits (\(1\) byte \(=8\) bits)
b = B × 8
b = B \times 8
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>b</mi>
<mo>=</mo>
<mi>B</mi>
<mo>×</mo>
<mn>8</mn>
</mrow>
</math>
b = B * 8
B*8
b := B*8;
b = B*8;
b = B×8
Website bandwidth (page views × page size × redundancy factor)
W = r × P × f
W = r \times P \times f
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>W</mi>
<mo>=</mo>
<mi>r</mi>
<mo>×</mo>
<mi>P</mi>
<mo>×</mo>
<mi>f</mi>
</mrow>
</math>
W = r * P * f
r*P*f
W := r*P*f;
W = r*P*f;
W = r×P×f
Hosting bandwidth (monthly data ÷ seconds in the period)
W = Q ÷ (d × 86400)
W = \dfrac{Q}{d \times 86400}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>W</mi>
<mo>=</mo>
<mfrac>
<mi>Q</mi>
<mrow><mi>d</mi><mo>×</mo><mn>86400</mn></mrow>
</mfrac>
</mrow>
</math>
W = Q / (d * 86400)
Q/(d*86400)
W := Q/(d*86400);
W = Q/(d*86400);
W = Q/(d×86400)
How to have ChatGPT do the calculation
You are a data transfer calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). Use decimal prefixes (1 KB = 1,000 B, 1 MB = 1,000,000 B, …) and 1 byte = 8 bits. How many seconds does it take to download a 100 MB file on a 10 Mbps (megabits per second) connection? Also give the answer in the form "X minutes Y seconds". Show the code you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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