MYT Study Studio / Free learning resource
Vector Components Calculator
Levels & boards: Years 10-13; IGCSE Extended to A Level / IB HL Cambridge, Pearson Edexcel, OxfordAQA and IB Maths / Physics. Vector and mechanics calculations.
Resolve vectors into horizontal and vertical components, recover a vector from components, or add up to six vectors. Switch between mathematical angles and bearings without losing quadrant information.
Made for independent learners in Hong Kong and across the GCC: the UAE (including Abu Dhabi, Dubai and Sharjah), Saudi Arabia, Kuwait, Qatar, Oman and Bahrain. Choose your exam board and syllabus, wherever you study.
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How to use the Vector Components Calculator
- Choose polar input, Cartesian components or a multi-vector sum.
- Select degrees or radians and confirm where the angle is measured from.
- Read both signed components and the resultant direction alongside the diagram.
A worked example
A vector of magnitude 10 at 150 degrees anticlockwise from +x has x=10 cos(150)=-8.660 and y=10 sin(150)=5. The negative x component is expected: the vector lies in the second quadrant. Two opposite equal vectors sum to zero, whose direction is undefined.
What to check before using your result
- All vectors must represent the same physical quantity and use the same units.
- An angle clockwise from north uses different sine/cosine placement from an angle anticlockwise from +x.
- Add components, not magnitudes, when vectors point in different directions.
Make your next practice session count
Use this result as a starting point, not a label for your ability. Record one error, explain its cause and complete a similar question without the worked answer. Then try a different example to check that you understood the method rather than remembered a number.
For exam-style application, choose the correct board and component in the MYT past-paper directory. For guided explanations, explore subject-specific online tutoring or request a free 30-minute demo.
Questions about this tool
Why is the resultant smaller than the sum of magnitudes?
Components can cancel. A resultant magnitude equals the sum of magnitudes only when all non-zero vectors point in the same direction.
What does the bearing convention mean?
North is positive y and east is positive x. Bearings increase clockwise from north; mathematical angles increase anticlockwise from positive x.
Do I need an account or need to send my results?
No account is required by this tool. Its calculations run in your browser. Tools with a Save on this device option store data locally only when you choose it; your browser, device policy and storage settings can affect persistence. Export important records before clearing browser data. This describes the tool, not any separate site analytics or contact-form processing.
Reference sources and scope
MYT provides independent learning resources, not official exam-board certification or school-entry decisions. Formula explanations, diagnostic questions and study plans here are original study aids. Check your current syllabus and official examination instructions before relying on a resource for an assessment.