Current Drawn on 5v rail on Arduino UNO R3

is 5v enough to run LCD1602 16x2 HD44780 I²C LCD and Solid State relay and and DS1307 RTC.
do I need to spend more to power this. or the 5v rail is enough

LCD is just some generic 16 character and two rows with I²C module.

the Solid State Relay is this OMRON 2/4/8-Ch 5V Solid State Relay | SainSmart – SainSmart.com

The RTC is just your typical RTC.

the power hog is the Solid State Relay about 160mA.

I currently power my arduino via cellphone USB Charger.

Hi, and welcome to the forum.

Morrisz:
the power hog is the Solid State Relay about 160mA.

I doubt that.
The two-channel module has the same supply rating as the 8-channel module.
I think the 8-channel module is about right. The 2-channel module would then be 40mA (when both on).
That (40mA) sounds about right for two relay optos + indicator LEDs.
Arduino pin current (relay input) is about 0.5mA.

An LCD uses very little current, but the backlight does.
Depending on the LED current limiting resistor value you use.
A RTC uses next to nothing.

A 5volt cellphone charger (connected to the USB socket) should be able to power all of this.
Leo..