Nothing built into TeamViewer restricts the transfer speed; if you're experiencing slow transfer speeds while using TeamViewer, this is a problem with your Internet connection or the connection of the recipient. You can make tweaks to your network and bandwidth use to ensure that you have the best possible speed. However, your top speeds can't be boosted without increasing your Internet plan.
Both your Internet speed and the recipient's Internet speed determine how quickly a file transfers between computers. On your end, as the sender, the speed is determined by your upload speed. Unfortunately, U.S. service providers have plans with high download speeds but only offer a small fraction of that speed for uploads. The speed is also hindered by the recipient's download speed. If you have an upload speed of 4Mbps but the recipient only has a download speed of 3Mbps, you won't be able to take full advantage of your speed.
Similar to the network speeds, you can only use so much bandwidth at once. If you're also hosting a video conference in TeamViewer, downloading files in your browser, streaming video or playing an online game, the speed of all your online applications suffers. Turning off any other bandwidth-heavy applications increases the bandwidth dedicated to your TeamViewer file transfer.
Opening a Port
For transfer speeds that fall significantly short of your maximum, you can try opening a port on your router to allow TeamViewer traffic to pass through unimpeded. For the most part, TeamViewer uses HTTP ports -- ports 80 and 443. You can also set TCP port 5938 open for outgoing traffic. If you're using a firewall, allow TeamViewer to communicate through your firewall. Windows comes with a built-in firewall; you can manage the settings by opening Windows Firewall in the Control Panel.
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If either computer involved in the transfer is connected via a wireless connection, the transfer speed isn't going to be at its peak. Wireless connections lose speed, with significant loss the farther you get from the signal source. Some routers also see a loss in speed due to power settings that reduce power usage and thus output. For the best possible connection and transfer speeds, connect both computers to the Internet via Ethernet cable.