Is Radha an incarnation of Lakshmi?

Popularly, yes. Many websites and murti descriptions call Radha an incarnation of Lakshmi. The older scriptures and the main Vaishnava schools put it differently. They describe Radha as Krishna's own hladini shakti, his internal energy of bliss, from whom Lakshmi herself expands. In the strict reading, the goddess who incarnates as Lakshmi is Rukmini, Krishna's queen in Dwarka, not Radha.

So the short answer people repeat is a simplification. The longer answer is more interesting, and it changes depending on which text and which tradition you ask.

Is Radha an incarnation of Lakshmi, or something else?

The claim that Radha is an avatar of Lakshmi is real and widespread. Wikipedia states it plainly: Radha is "the avatar of goddess Lakshmi" and also the hladini shakti of Krishna. You will find the same line copied across devotional blogs and temple pages.

The problem is that the two halves of that sentence pull in different directions.

An avatar of Lakshmi would make Radha a descent of an existing goddess, the same way Rama is a descent of Vishnu. The hladini shakti is not a separate goddess at all. It is Krishna's own energy of pleasure, the power by which he experiences bliss. If Radha is that energy, she cannot also be a copy of Lakshmi, because Lakshmi herself is a downstream expansion of it.

Most careful Vaishnava writing chooses the second reading. Radha is Krishna's internal potency, and Lakshmi is one of her partial forms.

What does each scripture and tradition actually say?

The picture only comes clear with the texts laid side by side, because each one speaks in its own register.

The row most pages skip is the first. The Bhagavata Purana is the central scripture of Krishna devotion, and it holds Radha unnamed throughout, which the acharyas read as concealment rather than absence. What it names is Rukmini, and it treats her as the queen who carries the fortune of the goddess Sri.

If Rukmini is Lakshmi, then who is Radha?

This is the exact question people keep asking, word for word, on Reddit and Quora. If Krishna is Vishnu and Rukmini is Lakshmi, where does Radha fit.

The Vaishnava answer is that Radha does not fit into that row at all. She is not a fourth deity standing next to Vishnu, Lakshmi and Rukmini. She is the energy of Krishna himself.

Bhagavata Purana 10.47.60, spoken by Uddhava and quoted in the Chaitanya Charitamrita, makes the ranking clear:

nayam shriyo 'nga u nitanta-rateh prasadah svar-yoshitam nalina-gandha-rucam kuto 'nyah rasotsave 'sya bhuja-danda-grihita-kantha- labdhashisham ya udagad vraja-vallabhinam

"When Lord Sri Krishna was dancing with the gopis in the rasa-lila, the gopis were embraced by the arms of the Lord. This transcendental favor was never bestowed upon the goddess of fortune or other consorts in the spiritual world."

Bhagavata Purana 10.47.60, translated by A.C. Bhaktivedanta Swami Prabhupada

The goddess of fortune is Lakshmi. Read closely, the Sanskrit names her and her alone: shriyah. The queens of Dvaraka enter only through the translator's phrase "other consorts", and through the Chaitanya Charitamrita, which ranks them separately. Either way the verse says plainly that the cowherd women of Vrindavan received something Lakshmi did not.

Radha is the foremost of those women. So the tradition does not lower her to Lakshmi's level. It puts her love above it.

The closest the Bhagavata Purana comes to Radha is a single line, 10.30.28, where the gopis notice that one among them "has perfectly worshipped" Krishna, since he left the others to be alone with her. Many commentators read that unnamed gopi as Radha, and some trace her very name to the word for worship in that verse. Even so, the text never names her, which is why her full identity had to come from later scripture.

Why is Radha worshipped with Krishna instead of Rukmini?

Rukmini is the wedded queen. Radha is not married to Krishna, and that is the point.

The Braj traditions treat Radha's love as pure longing with no contract behind it. No marriage, no throne, nothing owed back. That selfless love became the model for how a soul should love God, which is why the pair worshipped on the altar is Radha Krishna and not Rukmini Krishna. You can read how her story begins in the birth of Radharani.

Rukmini is not forgotten. Her marriage and her queenship are told at length in the Bhagavata Purana, and you can meet her and Krishna's other queens in the story of when Draupadi met Krishna's queens. But devotion made Radha the face of love, and Rukmini the face of the royal household.

Is Radha the same goddess as Sita or Saraswati?

No named scripture says so. On the forums you will see people connect Radha to Saraswati, to Sita, and to every form of the goddess at once, and it is easy to see why. If Radha is the root energy, then every goddess is a branch.

The Brahma Vaivarta Purana handles this with a clean list. It names five primary Prakritis, five faces of one supreme energy: Radha, Lakshmi, Saraswati, Savitri and Durga. In that scheme they are distinct, not identical. Radha is the chief consort of Krishna, Lakshmi is the goddess of fortune, Saraswati is knowledge, and so on.

Calling Radha "the essence of Sita and Lakshmi and Rukmini" is a devotional way of praising her as the source. It is not a claim that she was born as any of them. The same instinct sits behind the question of why Krishna never married Radha, where the schools again read one relationship in several ways. If you want to sit with her many names and titles, the thousand names of Radha collect them in one place.